Manager Arsene Wenger, who promised to have words with the player on Friday after saying he had damaged his reputation because of a newspaper picture of him with a cigarette in his mouth, was pleased with the England international's strike.
Wilshere had endured a poor first half against West Brom as he repeatedly gave away the ball and spent a lot of time picking himself up off the ground but he made up for it when his deflected 63rd-minute strike cancelled out Claudio Yacob's first-half headed opener.
"He had trouble today to find the rhythm of the game," Wenger, who played Wilshere out of position on the wing, told Sky Sports. "But he has character as well. He doesn't give up, he continues to play his game and got a great goal."
It was Wilshere's first Premier League goal in nearly three years and put Arsenal back on top of the table with 16 points from seven matches, ahead of Liverpool on goals scored.
"It was a tough game for me. I am not used to playing on the wing, I'm still getting used to it, I'm learning it, but I'm happy to do it for the team," Wilshere told Sky Sports.
"I got a goal which was nice, I've always said I want to score a few more goals."
He agreed it had been the ideal way to respond after being in the spotlight for the wrong reasons in recent days.
"When it comes to the weekend, you've got to do your job," he said. "There's thing that happen but at the end of the day we're footballers and we have to do our job."