Walcott came in for heavy criticism from the Arsenal fans at the Emirates Stadium as Spurs raced to an early two-goal lead.
But after the home side drew level, Tomas Rosicky and Walcott completed a comfortable fightback win.
Wenger confessed he thought about making a change when it became apparent Walcott was shouldering the blame for a disappointing start but believes the player’s performance demonstrated his value to the team.
“The crowd was starting to get on his back, and you wonder if you do him a favour if you leave him on,” said Walcott.
“But I felt that he is a player who can be straight, go behind the defenders, and nobody else is like that.
“He is a very direct player, and you know that sometimes he can miss a first touch and still considering the balance of our team I felt it was important to keep him in the side.”
Walcott admitted he had endured a difficult first 45 minutes but was satisfied with his response.
“You always have to get on with the game. When things are not going too well, I can hold my hands up and say I didn’t have the greatest of first halves,” he said.
“I was trying to forget about that and work hard in the second half.”
At Carrow Road, Ryan Giggs – playing in his 900th game for Manchester United – struck in the 90th minute to clinch a precious victory for Sir Alex Ferguson’s side.
United’s last-gasp 2-1 win over Norwich reduced Manchester City’s lead at the top to two points, Ferguson admitted it wasn’t the most impressive performance.
“I have to say we were lucky today, in the sense Norwich had more promise about them. I thought we were lethargic, too casual on the ball,” said Ferguson.
“Then when we lost the goal, we played brilliantly. That tells you something about the temperament, they do not get nervous and started to up their game, so that augurs well for us.”
Norwich would have had high hopes for a draw when Grant Holt pounced on 83 minutes to cancel out Paul Scholes’ seventh-minute opener at Carrow Road.
Meanwhile, Arsenal’s win eased the pressure on beleaguered Arsenal manager Wenger, whose side were still reeling from a heavy Champions League defeat to AC Milan and a FA Cup exit at Sunderland.
The Gunners’ victory also moved them back into the Champions League qualification places ahead of Chelsea.
“It was a performance full of everything you want from your team,” said Wenger.
“It had team spirit, technique, resilience. It was an exciting game, we had a difficult start but kept going and showed great character.
“When you’re 2-0 down against a team in front of you with the quality they have, you need something exceptional. We refused to lose today, we kept going and in the end I think we had too much quality and drive.”