Having knocked out holders Crystal Palace in the third round, the non-leaguers were beaten by a Sam Heathcote own goal on Monday as the Bees won 1-0.
Rooney said afterwards, "I'm so proud of my players for what they have achieved and the journey they have been on.
"I couldn't be any prouder. Unbelievable touch by their manager to come into our dressing room after full-time. It's been a bit of a whirlwind. Days like this is why you are involved.
"The lads were outstanding and the shape was really good. We train two times a week and we've put that performance on against a Premier League side.
"I started my football career at this club and I've started my managerial career at this club. We want to go on and get promoted. We want to try and get in the (National League North) play-offs."