The Foxes had struck the woodwork and missed several other chances in a one-sided first half at the King Power Stadium, and although Rovers improved in the second, the home side grabbed the only goal of the game 20 minutes from time through Jacob Blyth's bundled effort.
Rovers could have grabbed a point but for City goalkeeper Conrad Logan who made a fine fingertip save to deny substitute Dean Rittenberg late on, pushing the young striker's effort onto the foot of the post.
But that was as good as it got on a poor evening in the east midlands for the Under-21s.
"I'm disappointed really," said Kinder. "I thought with the side we had out that wasn't a good performance and not a good result for the players that were sat in that dressing room.
"I thought the second half was slightly better, their 'keeper has been forced to make a top class save from Dean Rittenberg.
"So there were a few positives to take out of it, Dickson has come through 90 minutes for the first time in a long, long time and we've Adam Henley, Darragh Lenihan, and John O'Sullivan all back.
"But I don't think there's many in the dressing room can sit there and say that they've had a good game, it is a disappointing one because we could have gotten something out of that game, but we didn't win enough battles.
"I think the effort is there, I can't criticise the effort, but we need to get the basics right."