Town looked set to claim three crucial points in their fight against the dreaded drop until Gareth Williams levelled for Forest in the dying seconds of the game.
After the game, Groves said: "I always felt Forest would get something out of the match because they kept knocking balls into our box.
"I would have settled for a point before the game, but when you get so close to winning all three it is obviously very disappointing.
"What we have got to do is translate that kind of performance into our home games if we are going to get out of trouble."
Nottingham Forest Match Report