The West Midlands outfit had fallen off the pace after failing to score in their previous four top flight matches, but Heskey reckons Saturday's win in the Cottagers' backyard proves Villa's Euro hopes are live and kicking.
"You see teams - top-four teams - go there and get outplayed but we really got at them and I think we deserved the points," Heskey, who referred to Fulham's victories over Manchester United and Liverpool, said in The Mirror
"Now we've got to try and keep our foot on the pedal.
"We always come bouncing back. We will never give up.
"Our confidence was high anyway because of the performances we had been putting in, but you've got to get the goals to go with that and against Fulham we did.
"They are a good side and they pass it around well.
"But we are all buzzing. We have some really great lads and we get on really well together. It's a nice atmosphere."
Barclays Prem To Be in Top 4 Win Outright: Aston Villa 7/2