Sam Wood opened the scoring with a thumping long-range strike on 70 minutes before top scorer Dean Morgan doubled their tally four minutes later.
Ainsworth admitted: "It was a very convincing away performance, one of the best away performances since I became manager and we scored some fantastic goals, which was a real bonus.
"Central defenders Gary Doherty and Leon Johnson seem to be forging this partnership of resilience and right-back Marvin McCoy's becoming a better player and Kortney Hause can't lose his place at left back.
"The back four were as resilient as anything, actually make that the back five as (goalkeeper) Matt Ingram took some awesome crosses and was called upon once for a fantastic save.
"I was really pleased with the way we had the better of the first half and kept a clean sheet against the wind. In the second half we were too much for them it was just a great sight to see Billy's goal drop in to make it 3-0. It just capped off a fantastic day for us.
"It was going to take something special to open it up because it was quite tight and Sam's goal opened the flood gates for us and it was a great strike.
"From then on I thought there was only one team in it. I thought we saw the game out really well."