Forest narrowly missed out on a place in the Championship play-offs after Anthony Knockaert's 90th-minute strike gave Leicester a 3-2 win at the City Ground.
The home side led inside three minutes through a Simon Cox goal but the Foxes replied through Matty James and Andy King.
Elliott Ward levelled proceedings early in the second half but Knockaert settled matters late on.
Forest assistant boss Kelly said: "I am extremely proud of the players, they have been absolutely brilliant.
"We had a right good go, we knew what was going on elsewhere and that we had to score. We went for it.
"This is stage one and step one of trying to get Forest back to where we all want them to be.
"The players showed pride in that performance. Don't forget that when we came in 15 games ago, we were in an extremely difficult position.
"If you had asked anybody if we could take it down to last moment of the last game of season, I'm sure everybody would have said that you are all mad.
"But the belief we all had in the squad, the desire and application that the manager has installed in every player and staff, we are extremely proud of that performance."