Wycombe will meet Plymouth in the play-off semi-final following their dramatic last-gasp 3-2 victory at Northampton.
Aaron Holloway and Nico Yennaris gave Wycombe the interval advantage. But Cobblers levelled through a Sam Wood own goal and Ryan Cresswell before Alfie Mawson’s stoppage-time winner.
Bury claimed the final automatic spot but Ainsworth said: “I don’t want any Wycombe supporter to be down because we’ve not got automatic promotion. This has been a great season, I’ve got a lot of pride in what we’ve achieved and this club has been turned around.
“Of course I would have loved to have nicked third place but this is still a great opportunity for us. I’ve got a bunch of players I believe in and we’ve still got a chance to make it a great season.
“It was always going to be a tough order for us to get the right result at both venues but I’m very proud of the players. It’s not in me or in my players to settle for a draw and we wanted to go for the win.
“This was a hard place to get a result but we set up to win the game and we did. It was a fantastic result but now we’ve got to get the week right to prepare for the play-offs.
“They are going to be two very tough games against Plymouth but we know what the prize is at the end of them. You’ve got to beat all the teams in the play-offs and you have to deal with whoever is in front of you.”
Wycombe could be without keeper Matt Ingram who had to come off at Sixfields through injury but Ainsworth added: “Hopefully Matt [Ingram] will be fit enough for the play-off games but I know what type of characters I’ve got in the squad and whatever team I put out will perform for us.”
Cobblers boss Chris Wilder admitted his side need to improve in both boxes if they are to mount a promotion push next season.
He said: “You end up where do you deserve to end up and we’ve got to accept that. We didn’t deserve to finish any higher and we’ve got a lot of work to do in the summer.
“It’s been an up and down season, we’ve been on the front foot in so many games but we end up getting done. If that’s down to fitness then we’re going to have to work much harder on the training ground.
“We have to be so much better going into next season. We don’t need massive changes in the summer but we have to improve in both boxes.
“We’re a positive team and we’ve played some really good football. But we don’t score enough goals and we need another striker to support Marc Richards and Ivan Toney.
“We need the results to match the performances. When some of my players watch the play-offs I want them to think about what might have been because they could have been in them.”
Looking back on the game, Wilder added: “The two games against Wycombe sum up our season. They’ve got four points out of six against us, they have a chance of going to Wembley and we haven’t.
“We should have come in 0-0 at half time but we were left chasing the game because of two pieces of poor defending. Wycombe showed the type of mentality in the first half which we need to show on the road.
“That was just another one in a catalogue of games we’ve seen up and down the country in which we’ve not been good enough in both boxes. We’ve played well in between but we can’t defend set-pieces and that has cost us points.”