Crewe skipper Matt Tootle missed the best chance of the game late on, while the relegation battlers ensured that City's dangerous strike-force of Emmanuel-Thomas and Sam Baldock had few clear sights of goal.
Tenacious work by Crewe striker Mathias Pogba in the 86th minute saw the ball break to Tootle unmarked eight yards out to the right of goal, but the right-back snatched at his shot and sent it well wide.
Cotterill said: "We passed the ball for fun, but without any penetration and you have to give Crewe credit for that.
"They have come here fighting for their lives and still made it a real football match.
"It was a bit of an anti-climax as far as we were concerned.
"If I am honest I have been expecting that sort of performance, with only pride to play for, and I'm glad we kept it until the penultimate game.
"Our crowd were fantastic, as they have been since I arrived.
"It has been a season of pressure and strain for the players and to reach 12th place in the table from where we were when I took over has been a fantastic effort by everyone connected with the club.
"We have a lot to build on for next season and I will be looking for one more performance at Crawley next Saturday.
"Then the lads will have earned their break."