Forest's play-off dream was crushed by east midlands rivals Leicester, who triumphed 3-2 to win at the City Ground in the league for the first time since 1972 and snatch sixth spot in the npower Championship.
Simon Cox put Forest ahead after three minutes but goals from Matty James and Andy King sent the Foxes into half-time ahead. Elliott Ward levelled things up at the start of the second half before Anthony Knockaert sent the 2,025 travelling fans - and the visiting bench - berserk in celebration.
"We are extremely proud of players. They were brilliant and we are proud of them," Kelly said. "Yes we are disappointed but look at where we've come from.
"When we came in 15 games ago we were in a very difficult position, so to take it down to last moment of the last game is some achievement. If we'd have said that would happen when we came in then you'd have said we were mad. We would have taken this when we first arrived.
"Now we can look forward to a full season next time round - a season with a full pre-season behind us. We'll sit down and talk to the chairman and the owners and see where we can improve over the summer."
Kelly addressed the media as manager Billy Davies took the unusual step of conducting his post-match media duties before kick-off at the City Ground.
Davies explained that he had "bigger fish to fry" and that he was showing the "utmost respect" to the journalists in attendance by holding the press conference before the game.
The Scot also said: "All throughout the season you guys (the media) are priority after the game - always.
"This is the last game of the season. We've sold over 10,000 season tickets, this is a day - in my opinion - where we have to show a huge thank you to the support of Nottingham Forest. Whatever happens, it's a celebration. These players have done fantastically well just to get us into this position."