Neil Harris ruefully admitted Gillingham missed the influence of club captain Shaun Williams as they went down to a fourth defeat in seven games.
Goals from Connor O’Riordan and Joe White secured a 2-0 win to move the Railwaymen up to third in the Sky Bet League Two table.
The Gills have dropped out of the top seven and their current form is in stark contrast to the blistering start they made to the campaign when they led the table in mid-August.
Harris rested midfielder Williams and felt others did not step up to the challenge to show the type of leadership exhibited by the missing 36-year-old.
“We went behind to the softest of goals and I’ve got to look at that and see if I’ve got the right players out there or whether I need to change the way I want to play,” said Harris.
“We’ve fallen short and it wasn’t through not creating chances. But whether the mentality was right in the group or whether there was enough leadership and desire out there without Shaun Williams, I don’t know.
“Shaun was missed badly tonight, but I rested him because of the way he carries himself when he plays 90 minutes at the weekend, which means he struggles to make a Tuesday night squad.
“He is such an important player for us, but people have to step up and take responsibility. We have to find it in ourselves to make sure that we come to places like Crewe and be harder to beat than that.
“Crewe have been excellent at home and are 13 games unbeaten. You have to give them credit for that, but this was a game we should still be winning.”
O’Riordan’s far-post header edged the Cheshire side ahead in the 30th minute after Gillingham had threatened early on when Ethan Coleman thumped against a post and George Lapslie fired over.
Defender O’Riordan finished off a Zac Williams cross as Crewe worked the ball back into the box following a corner.
Macauley Bonne should have levelled soon after when Robbie McKenzie’s shot was pushed into his path by goalkeeper Harvey Davies, only for the striker to fire the rebound wide with the net gaping.
Crewe held firm in the second half and the closest Gillingham went to levelling was when Coleman headed a corner wide.
The home side sealed victory when substitutes Aaron Rowe and White combined, with the latter netting his first goal of his loan spell from Newcastle with five minutes remaining.
Crewe boss Lee Bell said: “We had to work hard for that as Gillingham are a good team with an excellent manager. We rode our luck a couple of times in the first half and Harvey Davies made an outstanding save.
“But our shape was excellent and we really nullified them in the second half, and took our chance to seal it on the break. It was good to see Joe White tuck that away.
“I was really pleased with our defending against a team that can really hurt you. That is 13 games unbeaten at home overlapping from last season.
“We want to make the place a fortress and a hard place for teams to come to. But we also played some decent football tonight and we had some dangerous moments.”