Dario Gradi refused to be too critical of his side after the 1-0 defeat to Hereford and warned Crewe fans not to expect too much more from the squad.
Janos Kovacs - one of six debutants for the Bulls - scored the game's decisive goal after 16 minutes. Crewe pressed hard for an equaliser but were wasteful in front of goal, with Shaun Miller the main culprit.
Gradi said: "We were pretty decent and played some good football but they put us under pressure early on.
"I said to the players `there will be a lot of games like that where we are the better team but not by much`. We can't expect any team to roll over and die and we need to take our chances.
"I think we are playing pretty much to our potential at the moment and I don't think there is much more we can squeeze out of them. I think that is the best we can do, I'm afraid to say.
"They scored a good header, but I think we should have been marking him better. I just wish we could score headed goals like that. They defended well and we ran out of ideas in the end."