Danny Dichio headed Albion ahead after three minutes, and Arsenal were below par for the rest of the first half.
However, they were much-improved after the break with Francis Jeffers equalising three minutes into the second half, and Henry punishing a defensive error five minutes from time.
"After the first half we didn't deserve anything," the French international striker told Sky Sports TV.
"In the second half we had to show that we deserve to be at the top. We had to show another face of Arsenal.
"We were missing commitment and aggression but we did have that in the second half."
The win left Arsenal four clear of Chelsea at the top but Henry said the title race remained tight.
"If you miss out in one or two games it seems like you can be third or fourth," he said.
"It's going well but now we have to play Liverpool and Chelsea."
FRUSTRATED HOULLIER
Both those two were held to home draws on Thursday. Chelsea were goalless against Southampton, while Liverpool drew 1-1 with Blackburn Rovers to make it just three points from the last 24 and leave them nine off the pace.
"It is a test for our nerves and our character after eight games without a win and we feel extremely frustrated at times," said manager Gerard Houllier, whose team were four points clear at the top six weeks ago.
"I was hoping for a scruffy 1-0 today but we'll have to wait," he added.
After the stalemate at Stamford Bridge, Chelsea manager Claudio Ranieri became the latest premier league manager to praise Southampton.
"Southampton are good team, they have good organisation, they play busy football but they also fight for the second ball," said the Italian.
"They played a lot of balls into our area and it wasn't easy, though we did have some great chances at the end of the match."
Strachan agreed:
Middlesbrough are another side doing nicely in mid-table and moved up to eighth with their 3-1 home win over Manchester United.
"We've had tough fixtures, Chelsea, Arsenal and now Manchester United and we have done well in every game," said Boro manager Steve McClaren.
"Today the players were magnificent."
Alex Ferguson, McClaren's former boss at Old Trafford, was frustrated again after watching his team fail to turn possession into goals.
"It was a bad scoreline considering the possession we've had... I think in the first half we've really thrown it away," he said.
"The great opportunities on the edge of the box when we did make chances we didn't have the concentration to capitalise, then they get a breakaway and score."
Leeds United collected a rare win thanks to 16-year-old midfielder James Milner, whose equaliser in the 2-1 success at Sunderland made him the youngest scorer in the 10-year history of the premier league.
"I'm really pleased for him," said Leeds boss Terry Venables.
TALENTED BOY
"He's been in the squad for a few weeks but has only had a few minutes but he had a little bit longer today and he showed what he could do. He is a very talented boy."
Milner inherited the youngest scorer mark from Everton's Wayne Rooney, but the Everton forward remained in the limelight after getting sent off in his team's 1-1 draw at Birmingham.
However, Everton's scorer Tomasz Radzinski said the 81st minute red card after a clash with Steve Vickers with was harsh.
"I don't think it was a sending-off, not even a yellow card," said the Canadian.
"They both went for the ball and I think Wayne even won it...I hope he can be cleared."
Manager David Moyes agreed it was a harsh decision after "a whole-hearted challenge between two determined players.
"Maybe a little bit of reputation has gone before him (Rooney) and maybe the referee has been looking at that," added Moyes.
