Shrewsbury boss Graham Turner lamented a poor first-half display as his side bowed out of the Johnstone's Paint Trophy.
Alex skipper Luke Murphy fired the visitors in front in the ninth minute before Max Clayton doubled their advantage 12 minutes into the second half.
A huge error from goalkeeper Alan Martin gifted Shrewsbury substitute Asa Hall a goal but it was mere consolation as Crewe held on for a 2-1 win.
Turner, who turned 65 last week, said: "I thought first half we were sluggish, slow, didn't work hard enough and we conceded a poor goal. At least we had a go in the second half, we upped the tempo and played more at the pace we started the season at when we didn't get the results that some of our play deserved.
"But first half - and maybe it's just creeped in the last two or three home matches - we haven't worked anywhere near as hard or at the tempo that we have to. It was only towards the end of the second half that we gave it a go and we were a bit more positive.
"We imposed ourselves a little bit more on Crewe in that period but we allowed Crewe to dictate to us in the first half too much. To be fair, they've got some good, young players and they moved the ball about well, but we didn't half aid them in that first 45 minutes."