Tranmere boss Ronnie Moore praised his team's performance in the 2-1 victory at Chesterfield but blasted the timing of the Capital One Cup tie.
A superb strike in the 120th minute by Abdulai Bell-Baggie saw Rovers progress to the second round after Jack Lester had cancelled out Cole Stockton's extra-time opener.
Moore, who handed a debut to late loan signing Ben Gibson, was delighted with the result but questioned the scheduling of the first-round matches.
"I think we deserved it although the disappointing thing for me was that we had to go to extra time," Moore said. "But give our lads their due, we kept going and kept going and I don't think you'll see a better goal than Bell-Baggie's.
"We were the better side but the disappointing thing for me was why we are playing extra time on a Tuesday night. This should have been done on Saturday, everybody should have played Saturday and then we've got a free week to get ready for the first league game.
"We had six missing before the game and we've picked up a few knocks but I think we did alright and if we play like that in the league then I don't think we will be too far off."