Twice ahead against fellow Sky Bet League One strugglers, the hosts had to settle for a point thanks to a superb 80th-minute equaliser from Tranmere's Jason Koumas.
It was City's seventh game in 21 days and Cotterill said: "I feared that tiredness would be a factor and so it proved.
"At times we found it hard to raise a gallop, although we improved in the second half when we passed the ball a lot better.
"It has been a very tough period for the players and I'm pleased we now have a free week to prepare for another important game at Sheffield United.
"The lads are very disappointed in the dressing room and I take that as a sign of the progress we've made since I arrived.
"Not so long ago we would have lost that sort of game."
City went ahead with a fluke goal in the 12th minute. Sam Baldock controlled a Marlon Pack pass on the right touchline and saw his well-struck cross elude goalkeeper Owain Fon Williams, the ball going in off the far post for the striker's 17th goal of the season.
But Tranmere had started well and were level seven minutes later when James Wallace crossed from the left and Jake Cassidy turned past Aden Flint to drive a fierce shot over goalkeeper Simon Moore from 10 yards.
The hosts thought they had won it in the 78th minute when Baldock's chip from the right to the far post was headed home by left-back Derrick Williams for his first City goal.
But the least Tranmere deserved was a point on the balance of play and the classy Koumas had the final say with a sweetly-struck right-footed shot from 20 yards that found the top corner of the net.
- Sports & Recreation
- Jason Koumas
- Sam Baldock