Ryan Lowe scored a late winner to clinch a 1-0 win against League Two side Accrington and put Rovers in the hat for the second round.
And Moore thinks it will only give his side more confidence making progress in the Cup.
"I love the FA Cup and I think the players love it too," said Moore. "I don't see it as a distraction and it's great to be in the hat for the second round.
"We got to the third round last season and lost to Derby, but it's a great competition to be involved in.
"We were poor in the opening 20 minutes against Accrington and let them have too many shots, but we had words at half-time and we were a lot better defensively after the break.
"We were positive and put on forward options as we didn't want a replay and it was a hell of a finish by Ryan to win the game.
"I know if you give the ball to Ryan in those areas, he will score."
Moore also praised Jean-Louis Akpa-Akpro, who came off the bench and played the ball in which led to Lowe's winner, despite Stanley appealing for off-side.
"It was a great ball by Jean-Louis,"" Moore added.
"He has had a fair few injuries this season, but he has come on and made a difference and given us more of an attacking threat. I do have options now."
The defeat was hard on Stanley, who created the better chances in the opening half-hour with Tranmere keeper Owain Fon Williams having to be at his best.
James Gray had the first chance, clipping the ball just over the crossbar, while Kal Naismith's strike was saved by Fon Williams.
The keeper was in the action again soon after when Kayode Odejayi raced clean through, but the striker tried to take the ball around the keeper and Fon Williams got a hand to it.
Peter Murphy then fired just wide, Naismith forced another save out of the Tranmere keeper and Gray was not far off with a long-range effort.
The League One side did have a couple of chances before the break through Chris Atkinson and Jake Kirby and Lowe had the ball in the back of the net, but it was ruled out for off-side.
Both sides struggled to create clear-cut chances in the second half with neither keeper seriously troubled.
Rovers substitute Akpa-Akpro had a chance in the final 10 minutes, but headed wide before he found Lowe in the 90th minute for his winning goal.
- Sports & Recreation
- Ryan Lowe
- Owain Fon Williams