The Arsenal manager bemoaned his side's profligacy against the Baggies, but he did take great encouragement out of the performance of Jack Wilshere.
The hosts took the lead at the end of the first half through Claudio Yacob before Jack Wilshere drew the Gunners level in the second half. However, although Wenger said that a point was not a bad outcome against a strong Baggies side, the Frenchman was left ruing the chances missed by his side when the game was level.
"West Brom confirmed why they won at Manchester United because they have good players in every position and a huge squad," the 63-year-old coach told the press. "If you asked whether it was a fair point over the 90 minutes, I would say yes. We were 1-0 down just before halftime and, straight after halftime, [Nicolas] Anelka has the [chance to make it] 2-0 and that would have made it difficult after that.
"I have some regrets because, when we came back to 1-1, in the last half hour we had the chances to score a second goal but we showed spirit to come back and give it all and to try to win - but them as well."
Wilshere had been criticized by his manager after he was pictured smoking outside a London nightclub, so Wenger was keen to praise the midfielder for scoring his first league goal for the club since November 2010.
"Yes, at least that is done now," the Arsenal boss replied when asked about the statistic. "He had a difficult first half where he was fouled but he has shown that he has character and kept going. It was good that he was rewarded. He was pushed over a lot. I don't think it was dirty but he was pushed over a lot and he didn't get the fouls. In the second half he gave some great balls and, overall, he had a very good second half.
"I think he learns very quickly and what is more interesting for England than for Arsenal is that he shows the right response on the pitch. I don't think he will ever be a 'goalscorer.' He's a player who can create chances and provide chances for others - that is important in our job. It's good that he knows that he can score."