The point has seen Arsenal go back to the top of the Premier League table after seven matches.
"It was breathless," BBC Sport quotes Wenger as saying. "West Brom showed why they won at Manchester United last week and we had a hell of a task to come back but we showed character and we had chances to go on an win it.
"They are strong on the break, they are quick and go forward with some quick players. We tried desperately to score the second goal and we had the chances late on to do it."
Arsenal return to Premier League action on October 19 when they welcome Norwich City to the Emirates Stadium.