Wycombe moved to the top of Sky Bet League One with a comfortable 2-0 victory over Tranmere at Prenton Park, but the game was marred by an alleged incident of homophobic abuse aimed at Wanderers goalkeeper Ryan Allsop.
It is understood that Allsop reported homophobic abuse to the referee during the interval after the Chairboys keeper had kept goal at the Kop end in the first half.
Speaking about the alleged incident, Ainsworth said: "If that's the case then for me there are some stupid idiots about.
"Whether it's racist or homophobic, whatever it is, we have to stamp this out.
"I have got to credit Ryan Allsop for being brave enough to stand up and say I'm reporting this, and that's what we are and I'll stand by him."
Moving his focus back to the football, he added: "I'm so proud of the boys. Inside the dressing room we keep private what we believe we can achieve and what our ambitions are.
"To improve on last year was always the aim. We're really proud of where we are and deservedly so.
"It was a tough game, not just because it's Tranmere away but because we've got them three times in a week. We've scored two more set plays at Tranmere. They're going to be sick of our set plays."
Akinfenwa was on the bench when the two sides met in the FA Cup here last weekend but, when Jacobson found him unmarked in the Rovers penalty area, his goal was a formality.
It got worse for Tranmere two minutes later when Darren Potter brought down David Wheeler in the penalty area, gifting Wanderers a spot-kick that Jacobson confidently converted on his 500th career appearance.
Micky Mellon made half-time changes but, despite the efforts of Morgan Ferrier and Corey Blackett-Taylor, the 18th-placed hosts missed the opportunity to gain breathing space over the teams below them.
Mellon said: "We knew the threats that we were going to face – Akinfenwa and free-kicks. To be undone by the things that you're absolutely 100 per cent sure you're going to have to be good at is really frustrating.
"Sometimes when you come up against teams and they have some good play and things that you haven't seen in games that you've played against them before, you have to say that's football because football can be random, but there's nobody telling me that they came to the game today and never thought that there's going to be direct play from free-kicks.
"When you know that they're coming in, it doesn't take a rocket scientist to see that you're going to have to be lively around Akinfenwa."
On the allegation of homophobic abuse, Mellon added: "What I do know is Tranmere is a club of great values. We know what's right and what's wrong. If people are proven to have done the wrong thing then they will be suitably punished as much as they can be."