Steven Davies put the skids under Forest with a 50th-minute shot that took a deflection after being allowed to turn in a crowded penalty area.
Twelve minutes later midfielder Marvin Elliott, who had only arrived back from playing for Jamaica in Mexico on Wednesday 24 hours before the game, rose to head in a Stephen Pearson free-kick.
Forest lacked a cutting edge. Dexter Blackstock headed against the crossbar from their best chance after 23 minutes and Billy Sharp was denied by a brilliant Tom Heaton save in the second half.
Billy Davies, who takes over as Forest boss on Monday, elected to miss the game, leaving Kelly to face the media.
"The biggest job for Billy will be to sort out the team's inconsistency because that has been our main weakness," said the caretaker boss.
"By looking at it coldly from the outside I am sure he will be able to come up with some ideas. Those of us close to the players know there is no problem with their level of commitment.
"We started both halves well and on another day Dexter would have scored with his header. But we defended poorly for the first goal and were disappointed to concede the second from a set-piece because we work hard on them.
"I am sure Billy was taking in another game. He will study this one on DVD and in any case he knows a lot of the players very well."