The 59-year-old was disappointed that his side were unable to get a result at Old Trafford on Wednesday, but promised that they would be stronger in their home ties
Sir Alex Ferguson's men emerged victorious thanks to an early goal from midfielder Michael Carrick, while Nani went on to miss a penalty, but the match was closer than many expected and the coach could not hide his frustrations about the result.
"We played well in general but I am upset about the defeat," Terim told reporters.
"We showed our game strategy time to time. At the beginning, we were a little bit nervous but later on we balanced.
"We could have conceded more than one goal. But also, we could have scored an equaliser and beaten Manchester United as well.
"Physically the team did well but we were unlucky in the final touches. Galatasaray have started to play on a different level now and we must develop ourselves.
"I am glad that we fought back against Manchester United but I am upset because we couldn’t reflect our performance in the score."
With Manchester United the early favourites to secure progression out of a group that also includes Braga and CFR Cluj, Terim remains bullish on his side's chances, as he is confident of picking up a positive result in the reverse fixture later on in the campaign.
"We wanted to return Turkey with a good result, but my team will continue to work and study this match and learn our lesson," he added.
"Manchester United will be more uncomfortable when we play in Istanbul."