Despite Jose Mourinho describing the performance as one that lacked 'class and personality', Lingard elected to be more positive.
"Brighton sat back and hit us on the counter-attack a few times, which we were obviously aware of before the match, but we knew we needed to win and we got the win, which was the most important thing," Lingard said to 'manutd.com'.
"Of course (confidence took a knock after Tuesday night). It's always difficult for a team to be knocked out of a competition, but we showed the character to bounce back and not let anything faze us.
"Semi-finals are always big and it's like the final, you could say, at a neutral ground, so we're excited.
"Any opportunity to win a trophy is always good for the team and the fans, so if we can get a trophy out of the season, it'll be good.
"The semi-final keeps everyone motivated and we have something to look forward to, but saying that, in the Premier League, we need to maintain that second spot and keep the pressure on at the top."
Manchester United joined Tottenham in the hat for the semi final draw, with the other two quarter finals taking place on Sunday.