The Gunners boss also praised the attitude of his players in the second half of the season to lift themselves into contention for third place and finally put their dreadful start to the season behind them.
“I’m very proud of this season because we were not only tested on the field but also off it as a club,” he told reporters after the match.
“The solidity and unity inside the club were really deeply tested and we didn’t show any weakness and kept united and in the end we came back. It’s a good lesson for everybody.
“We have qualified 15 times now for the Champions League - there are only three clubs who have done that in Europe - that means it is not as easy as it looks.”
Wenger was particularly happy with his side’s second-half comeback in the season as they rose from the lower echelons of the table to compete with north London rivals Spurs for the automatic Champions League place.
“I think if you look at the season as a whole we have only lost only two games out of the last 16,” the Frenchman continued.
“We have created a fantastic run and in the end we have finished with 70 points - that is respectable and we qualify straight away to the Champions League.
"Fifteen consecutive years, of course we are very proud of that. Especially this season, starting from where we started from.”
Arsenal were given a gift early in this game as Marton Fulop made a mess of collecting a ball on the edge of his penalty area which allowed Yossi Benayoun to steal the ball from him and tap it into the empty net.
However the Baggies came back strong and scored twice in four minutes to put Arsenal in jeopardy of only finishing fourth, but Andre Santos got his side back into the game with a swerving shot after 30 minutes which levelled the scores going into the break.
Early in the second half the Gunners were gifted another goal by Fulop as his attempt to punch a Robin van Persie corner away went back towards his goal and Laurent Koscielny had the easy job of heading the ball into the net.
Wenger admitted there were times during the game his side did not look at their best.
“I felt once we went 1-0l up we were nervous and shaky,” he said. “When we were 2-1 down we got back to our game again and in the end we just hung on because we defended on crosses with resilience
“I am still not thanking the referee for the five minutes of added time because my heart suffered too much.”
The victory caps a rollercoaster of a season for Arsenal, and Wenger revealed that there were times he was uncertain his side would make it into the top three.
“In September certainly not,” he admitted. “We were 17th in the league in September and in our first seven games we had lost four.
“When you have played seven and lost four and you have 31 games to go you think it is very hard to compete to finish third but we had an exceptional run after our exit from the Champions League.
“I didn’t want to finish fourth because fourth if Chelsea win the Champions League you’re not in it, and even if they don't win you are not straight into the Champions League because you play a qualifier, which makes it more difficult.”
The travelling Arsenal support celebrated with the players at the end of the game and captain Van Persie was the last man out with them, but Wenger didn’t feel that it was a sign of the striker’s departure.
“If a player doesn’t go out and celebrate they say he is already gone,” he added.
“If he does go out and celebrate they say he is saying goodbye - I believe it is a positive sign.”