A defensive error led to Charlie Kirk opening the scoring after just five minutes before Tom Lowery sealed the win in the second half after Adel Gafaiti had been shown a red card for an off the ball incident.
Suffering a second successive defeat, both Macclesfield and Notts County also suffered losses to keep a status quo at the bottom of the table going into Easter Monday’s fixtures.
Despite the disappointing trip to Cheshire, Town’s boss feels the Glovers still are in the running for safety.
“One of the boys said it might go to the last game, and it does look like that because we’ve got out of jail for the third week on the bounce.
“We’ve got a chance on Monday to jump above those two as they’ve got two hard games. It could go all the way to the wire.
“Actually I think the goal difference got a bit better for us. But we’ve got to get a result, that changes the situation and gets some positivity in the squad, so you get a bit of confidence back.”
Enjoying bright spells at Alexandra Stadium, Gafaiti’s dismissal on 57 minutes at 1-0 down saw the Alex enjoy a resurgence in momentum.
Penning the green and whites in for the remainder of the match, Marmon still felt there wasn’t much in the match.
“I think that after the goal we matched them. But then once we had the red card and the second goal went in and we were really pushing up, we were lucky we didn’t concede any more goals.
“With a side like Crewe they’ve got nothing to lose. They’re not going anywhere. I think that they picked their game up, but we actually got back into the game. We didn’t really threaten, but we were back in it, and there was only one goal in it.
“I think that if the fans are not deterred by the result, we’ve still got a massive chance to stay in the Football League. To get behind us on Monday – and I can’t stop saying that. There will be a situation where we get a chance to go a goal up and hopefully, we will do that on Monday for us.”