The German is 40 points adrift of Mercedes rival Lewis Hamilton with six races remaining and is running out of time to reassert himself in the battle of the four times world champions.
The Mercedes driver, who fought back from last to second after being sent spinning at the third corner by Ferrari's Finn, had spoken immediately after the race of the Italian team's 'interesting tactics'.
Ferrari are unlikely to have the fastest car when the Formula One season starts in Australia next month but they hope to be close enough for Fernando Alonso to make the difference, according to team principal Stefano Domenicali.
Australian Daniel Ricciardo won the Chinese Grand Prix for Red Bull on Sunday while Ferrari's championship leader Sebastian Vettel finished only eighth.
Stefano Domenicali resigned as Ferrari's Formula One team principal on Monday, and the company's North America president and chief executive Marco Mattiacci was appointed as his replacement.
Summary of sports events and persons who made news on Monday
The German, whose bid for a fifth crown petered out last year in mistakes and misfortune, had already been facing questions about whether he was making too many errors to win the championship.
The five-time world player of the year opened his account in the easiest possible fashion by tapping into an empty net from less than two metres in the 50th minute.
Hamilton held off a mid-race challenge from Red Bull's Max Verstappen to register a record-equalling fourth triumph at the floodlit Marina Bay Street Circuit track, while Vettel finished third to slip further behind in the title race.
Kimi Raikkonen will race for Ferrari next season after agreeing a two-year deal that takes the 2007 Formula One World champion back to the glamour team he left in 2009.
Fernando Alonso indicated his Formula One future was in his own hands despite Red Bull announcing on Saturday that four time world champion Sebastian Vettel was leaving to join Ferrari.
Champions Mercedes are chasing a sixth successive double, and Lewis Hamilton his sixth drivers' title, but the task looks tougher than ever.
Red Bull's Dutch 20-year-old Max Verstappen took the chequered flag in second place with Kimi Raikkonen completing the podium for Ferrari and Australian Daniel Ricciardo finishing fourth for Red Bull.
Ferrari's Formula One world championship leader Sebastian Vettel was handed a five-second penalty for colliding with the Mercedes of Valtteri Bottas on the opening lap of the French Grand Prix on Sunday.
Summary of sports events and persons who made news on Friday
The 2019 Formula One world championship starts on March 17 with 21 races in a season that ends later than any since 1963.
Ferrari felt the pain on Sunday after emerging with just two points from a hard day in front of their home fans at the Italian Grand Prix.
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Team mate Sebastian Vettel was second fastest to complete the front-row sweep, with championship leader Lewis Hamilton third for Mercedes.
Ferrari dealt Fernando Alonso a rare public rebuke on his 32nd birthday on Monday for critical comments after Sunday's Hungarian Formula One Grand Prix.
Ferrari are considering whether to lodge a protest that could lead to the result of the Formula One world championship being overturned.
Formula One breathed a sigh of relief on Sunday after the sport's new 'halo' head protection device saved Charles Leclerc from what might have been a potentially serious impact.
Four times MotoGP world champion Marc Marquez drove a Formula One car for the first time at the Red Bull Ring in Austria on Tuesday but said his focus remains firmly on two wheels for the next few years at least.
Daniel Ricciardo kept calm and carried on to win a tense Monaco Grand Prix for Red Bull on Sunday after power unit problems threatened to wreck his hopes of victory in Formula One's showcase race.
Jose Froilan Gonzalez, the 'Pampas Bull' who in 1951 became the first driver to win a Formula One world championship Grand Prix for Ferrari, has died in Buenos Aires at the age of 90, Argentine media reported on Saturday.
Ricciardo, in blistering form since Thursday practice around the streets of the tiny Mediterranean principality, made sure of the top slot for his team's 250th race start with a quickest lap of one minute 10.810 seconds.
The International Automobile Federation (FIA) has summoned Mercedes and tyre supplier Pirelli to its international tribunal in Paris on June 20 on charges of breaking the rules by testing in Spain last month.
'I'm so grateful for everyone who helped me be here, to raise the bar and lift the cup'
'Renault Sport Racing managing director Cyril Abiteboul told reporters that Ricciardo could be the spark needed to ignite the team on track'
Italian doctor Michele Ferrari denied on Tuesday accusations from the US Anti-Doping Agency (USADA) that he masterminded a doping programme for American cyclist Lance Armstrong.
Quite a few teams and captains have already been fined for slow over rate this season.
Formula One's governing body put Ferrari, the sport's most successful team, in the spotlight along with Mercedes on Friday in an investigation into alleged breaches of the testing regulations.
A summary of sports events and persons who made news on Thursday
The last time Kimi Raikkonen stood on top of a Formula One podium, Lewis Hamilton had just joined Mercedes with one championship to his name and Sebastian Vettel was riding high with Red Bull.
Summary of sports events and persons who made news on Monday
A summary of sports events and persons who made news on Wednesday
Ferrari's new team principal Marco Mattiacci was taken by surprise when Luca di Montezemolo offered him the top job at Formula One's glamour team, the Italian initially believing the chairman's approach to be a joke.
'Yeah let's take Modi out with a sniper rifle,' is a line from a conversation cited in the chargesheet, attributed to an associate of Ubed Ahmed Mirza.
The father of a nine year-old boy, who drove a Ferrari F 430 recently with his five-year-brother along side, causing widespread outrage, was arrested on Monday and released on bail.
Formula One world champion Lewis Hamilton won the Hungarian Grand Prix from pole position for Mercedes on Sunday to go into the August break with a 24-point lead over Ferrari rival Sebastian Vettel.