Arsene Wenger was delighted that his revitalised Arsenal team were able to seal third place with a victory at the Hawthorns.
Despite a wretched start to the campaign Arsenal recovered to book a Champions League place for the 15th season in a row.
Yossi Benayoun put Arsenal ahead, but West Bromwich Albion responded with goals from Shane Long and Graham Dorrans.
The Gunners remained cool, though, as Andre Santos equalised before Laurent Koscielny grabbed a second half winner and Wenger was satisfied.
"I think if you look at the season as a whole, we lost only two of the last 16 games and created a fantastic run. In the end we finished with 70 points, which is respectable, and we qualify for the Champions League for the 15th consecutive year.
"Of course we are very proud of that, especially this season having started where we started. We had problems getting over the line and you could see that again today.
"When we were 1-0 up we were nervous. When we were 2-1 down we got back to our game again and in the end we just hung on. We defended crosses with resilience but as long as we did not manage a fourth goal I was nervous. I am still thinking of suing the referee for the five minutes of added time because my heart suffered immensely!
"We were 17th in the league then and in the first seven games we had lost four. When you have played seven games and lost four you think there are 31 games to go and it is very difficult to imagine that you will finish third. But we had an exceptional run after our exit in the Champions League.
"I don't know if it is one of my best seasons, I leave that to you. I am very proud of this season because we were not only tested on the football front - which as a Club we are used to - but on our mental solidity, unity and solidarity within.
"We were deeply tested, we did not show any weakness, kept united and in the end came back. It is a good lesson for everybody. At some stages everybody was wondering what we were doing."