Mark Cullen’s fifth goal in six starts was enough to secure Pools’ place in the second round of the competition on Tuesday evening.
Pools will now head to League One Lincoln City on December 4 in the second round of the competition.
Reacting to the defeat, Ainsworth said: "We've had chances and really there's little threat from them, just two shots that were worrying and one of them went in.
"That's the game sometimes. The only thing we can do now is focus on Bolton on Sunday.
"At some stage somebody is going to take a beating off us, these chances are going to go in. These opportunities that are coming will get scored.
"I'm gutted for the boys, they're an unbelievable bunch and I have total belief in them."
On the match, caretaker boss Antony Sweeney said: “It's what we asked for and what we thought we might need to get through. The lads, to a man, were absolutely fantastic.
“We rode our luck at times, probably too much for our liking but you don't come away from a place like this with a win and a clean sheet without riding your luck.
“We want more bodies into the box and the ball goes into the area and Culls is in the right area again and does well and continues his great run for us.
“You could go through the full team. It's not easy for 95-minutes of getting the ball loaded into the box, Wycombe are very good at what they do but we stood up to it brilliantly.”