Victory over Newcastle confirmed their Champions League qualification for next season.
Sunday's win marked Arsenal's final home game and Odegaard addressed the fans on the pitch afterwards.
"We can be very proud of what we’ve done, especially in the Champions League," he said. "I think we had a great run and had some great experiences there.
"We have to admit that we haven’t been good enough in the league but I think we just have to take all the experiences, good and bad, and take them into next season and make sure that we come back better."
The stadium was on fire
Odegaard rated their Champions League quarterfinal win against Real Madrid as the season highlight.
He said: "Those are the nights that we live for, to play here at home with that support, the stadium was on fire, great game, hopefully we can have many more moments like that next season so it’s unbelievable to feel that support and the love from you guys.
"We want to say thank you for the support, we always feel the love when we come here to the stadium and the support we have is amazing so thank you so much. We have to use all the experiences from this season, good and bad, feel that pain of not winning and take into next season and make sure we come back stronger and bring trophies to this club."