Wimbledon came closest to a winning goal but striker Adebayo Akinfenwa’s first-half header rattled a post as the Chairboys kept their 15th clean sheet of the season.
Injury-ravaged Wycombe ended the game with 10 men when Aaron Pierre was sent off while wins elsewhere for Bury and Southend leave their top-three place in some doubt.
But Ainsworth said: “We’re still the ones to catch. They have to pass us before they can consider themselves as promotion candidates.
“At the moment we’re ok. We’re still in third place and it’s a great battling point for us.
“We’re stretched to the limit here and it’s going to be tough next week to get everybody ready but the spirit we’ve shown has been fantastic.
“Four players were playing out of position, so to get a point away at a tough place to come I am really proud of the players. Every one of them gave everything and so did the fans.
“For this club to have made the play-offs is an absolutely unbelievable achievement after last season.
“Whether we can do it or not we’ll see. We’ve got a huge game against Morecambe next Saturday and hopefully there will be a few twists and turns yet.”
Wycombe named only five substitutes of a permitted seven, such is the depth of their injury strife. And when Matt Bloomfield left the pitch after just seven minutes it looked as though it might not be Wycombe’s day.
But they earned a draw after Akinfenwa was denied by the woodwork and then by referee Trevor Kettle, who chose not to point to the spot after the big striker looked to have been bundled over inside the box.
Wimbledon boss Neal Ardley said: “We win the game if the referee makes the right decisions. The foul on Bayo is the most stonewall penalty I’ve ever seen.
“I’ve been in to see the referee and told him in a nice way it’s the worst decision he will ever make and he said he will have a look at it. But how you don’t give a penalty I don’t know.
“The goal he disallows, you watch Bayo and Pierre and couldn’t tell who was fouling who. Bayo’s stronger, wins the header and we score.
“Both of them were wrong and it’s disappointing because this season more than ever I’ve felt the standard of refereeing has been at its worst.
“I’ve got to be careful what I say but it has been at its worst for the whole season and I know a lot of other managers feel the same way.”