Adam McGurk netted the winner for Rovers 12 minutes into the second half after Cole Stockton had cancelled out Liam Cooper's opener for the visitors.
"We are disappointed as we missed out on a chance to get extra revenue for the club and get a big tie in the next round," Cook said.
"It hurts but the defeat gives us a chance to concentrate on the league and we need to improve our mentality now. We want to try and achieve promotion and we have 26 cup finals to play before we can achieve that.
"Competition for places is good but we have a long way to go and we know what we want to do from here on in.
"Tranmere played good football in a good spirit and they were very competitive but we gave bad goals away. The lads who made mistakes will certainly learn from them. It probably wasn't Tranmere's best performance of the season but good teams find a way to win and we wish them luck in the next round."