A second defeat under Dougie Freedman came after an impressive display from the home side, goals from Howson, Jerome and Hoolahan before a Chris Burke consolation for Forest.
Norwich manager Alex Neil hailed what he called the best performance under his reign and felt that the Canaries 'dominated' the match as they hauled themselves back into automatic promotion contention.
Freedman, however, refused to throw in the towel on a top-six finish and is already looking ahead to the Easter double-header against Wolverhampton Wanderers and Brentford, the two sides currently directly above the Reds in the table.
"If we can take six points from those, who knows what might happen," said the Scot afterwards.