The Welsh side, who dominated for long periods of the game, currently sit ninth in the Championship and have attracted praise for Roberto Martinez's attractive style of play, with Sir Alex Ferguson one of the most recent admirers.
Ferguson's side, Manchester United, await the winners of Tuesday's game, with Gower keen to use the Scot's encouragement as an incentive.
"We can beat Fulham without a shadow of a doubt - and that's not just us saying that," he told Wales Online.
"When you hear someone like Sir Alex Ferguson saying what he did you know you must have a chance.
"Sometimes you question yourself whether you're playing as well as you think, but then you hear what people like Sir Alex say and the TV coverage, and realise we are that good at the moment and we have nothing to fear.
"Even talking to (Fulham midfielder) Simon Davies after the first game, he was saying how frustrated he was because he hardly had a kick and had to chase shadows for 90 minutes.
"If you can do that to a Premier League team then it says something and we can't help but take confidence from that."
Another factor spurring Gower on is the memory of the opportunities he spurned in the 1-1 draw last time out.
Gower saw two gilt-edged chances go begging and the 30-year-old admits he is desperate to make amends at Craven Cottage.
"I know I played well and I was pleased with that. But when you miss a chance like I did against Fulham then it's not about you, it's about costing the team - and that sticks in your throat," he said.
"To be fair, I think I've been unlucky so far this year but that was my first one I should have put away.
"Then when Manchester United comes out of the hat you can't help thinking that if I had put that in then we would be in the quarter-finals.
"Or even if I'd just had a bit of luck off the post we could be looking forward to one of the biggest games of our careers. And that's what's getting to me."
Gower started his career with Tottenham but spent time with Barnet before making over 200 appearances for Southend, and having done his time in the lower reaches of the Football League he is fully aware just what a tie against Manchester United would mean for his fellow players and the club.
"At first we were hoping for another lower-key game because you see what Cardiff and Barnsley did last year and you start dreaming," he added.
"But then United come out and you realise you're one win away from such a fantastic opportunity and a game against the best team in the world.
"I'm 30 and I know there might not be many more opportunities like this. We know if we go to Fulham and perform as we know we can that chance is there for us."