Igor Jesus slotted through a crowd two minutes from time to clinch a first away victory in Europe for Forest since 1995.
Paulo Dybala scored his first Serie A goal of the season to give Roma a 1-0 victory at Sassuolo on Sunday to lift them level on points with leaders Napoli.
The French side led through an early Hakon Haraldsson goal in the Italian capital but Roma had the chance to equalise late on after a handball by Aissa Mandi.
Inter Milan followed up on a positive start in the Champions League by beating Sassuolo 2-1 on Sunday to put their Serie A season back on track.
New AS Roma coach Ivan Juric said his players were disappointed by the sacking of Daniele De Rossi, but he was pleased with their performance as they clinched their first Serie A win of the season by beating Udinese 3-0 on Sunday.
AS Roma have sacked head coach Daniele De Rossi after the club went winless in their first four league matches of the season, the Serie A side said on Wednesday.
Last season's runners-up Roma advanced to their fourth European semi-final in a row.
Play in Roma's Serie A match at Udinese on Sunday was abandoned after Evan Ndicka collapsed with an apparent problem with his chest.
Roberto De Zerbi revealed his regrets on Italian television after Brighton were swept aside 4-0 in the Europa League on Thursday night.
Last season's runners-up Roma advanced to their fourth European semi-final in a row.
Play in Roma's Serie A match at Udinese on Sunday was abandoned after Evan Ndicka collapsed with an apparent problem with his chest.
Roberto De Zerbi revealed his regrets on Italian television after Brighton were swept aside 4-0 in the Europa League on Thursday night.
Adrien Rabiot's second-half goal earned Juventus a 1-0 home win over AS Roma on Saturday that took them within two points of Serie A leaders Inter Milan.
AC Milan, meanwhile, were drawn against French club Rennes.
Roma have just one win from their six league matches so far.
AS Roma head coach Jose Mourinho has been suspended for their next four matches in the Europa League after the Portuguese boss directed abusive language at referee Anthony Taylor while the club was fined, Europe's soccer body UEFA said on Wednesday.
His message was one of pride, which is what he has restored at Roma, a team which has one of Italy's largest, most passionate fan bases but has won little of note since being founded in 1927.
AS Roma coach Jose Mourinho said he was not fixated on becoming a legend at the club after leading his side to a second straight European final with a 1-0 aggregate win over Bayer Leverkusen after their Europa League semi-final, second leg on Thursday.
AS Roma boss Jose Mourinho is keen on coming to Paris next season and replace Christophe Galtier after Luis Campos held talks with his agent.
