Clayton Donaldson, who had already hit the woodwork, netted his 20th goal of the season as he left defender Gregor Robertson in his wake before converting with a low finish.
The home side came under immense pressure, Danny Whitaker hitting the upright, before Danny Shelley converted a late free-kick to secure the points.
Sheridan said: "All credit to Crewe but I actually thought we were the better team. I thought we played well and was more than happy with the performance. I don't expect us to win every game as long as we play well and I'll take the defeat on the chin.
"Other results have gone our way which is a bit frustrating because we could have gone further ahead but I can't complain because the lads have been brilliant for the last four or five games. We move on and hopefully we will get a response against Rotherham."