Manager Les Parry hailed a much-improved Tranmere performance after his side recorded their first win of the season at Walsall in the Carling Cup.
A solitary 40th-minute goal from Ian Goodison saw Rovers safely through to the second round. The defender finished from close range when Joss Labadie headed a free-kick from Paul McLaren across the face of goal.
Parry, who saw his side begin their League One campaign with a 2-1 home defeat to Oldham, said: "We said before the game we thought all 11 lads had something to prove after Saturday's performance because I'm sure they all felt they could do better and, to a man, everyone did better.
"I am much happier but I was not too down after the home defeat by Oldham because that reflects on the players and affects them."
Parry also praised the attitude of striker Ian Thomas-Moore, who has handed in a transfer request, adding: "We could not replace him.
"He will always put in a performance and the fact that he has put in a transfer request won't change his attitude. I did not hesitate in leaving him as captain."