The Japan international says that a good result in the away leg will be crucial if the Red Devils are to progress but expects a tough test against the Greek champion.
The hosts have lost just once at home all season, a 2-1 defeat to PSG in the Champions League in November, and currently lead the Greek Super League by 20 points.
In stark contrast, United is a distant sixth in the Premier League but topped the qualifying group and is yet to taste defeat in Europe this season.
Kagawa, who has not featured for the Red Devils since January's defeat to Sunderland in the Capital One Cup, feels that a good result in Greece is crucial if his side is to progress, telling the club's official website: "When you get to this stage in the competition you can't afford any slips-up or you're out.
"The away leg is very important - we need to get a good result there. We have a lot of experienced players in our squad who will hopefully help us to achieve that."
The Japan international also says that his team is determined to improve on last season, when it was dumped out of the tournament at this stage by Real Madrid.
"Our Champions League campaign ended at the last-16 stage last season so we want to go further this time," he added.
"Olympiakos are a good team and there are no easy games in this competition - we all know that - so we have to prepare as well as we can."