Goals from Daryl Murphy and Freddie Sears, either side of a Christophe Berra own goal, gave play-off chasing Ipswich all three points meaning they only need a point next weekend to secure a top-six place.
Forest are 12th ahead of their season finale against a Cardiff City side directly below them in the table.
Speaking to the official NFFC website after the game, Dougie Freedman felt his side again showed the lack of a 'killer instinct' to take control of games where they are on top.
"Unfortunately it’s the same story – perform very well, show great attitude and commitment, but come up a little bit short."