Hyypia's side will travel to Old Trafford to meet Moyes' Manchester United with both coaches making their first appearance in Europe's pinnacle club competition.
But the Finnish coach insists that United's history in the tournament means Leverkusen can relax and enjoy the occasion.
"I think David Moyes has a little bit more experience in this area of football and he's the manager of this big club here in Manchester," Hyypia said.
"They are playing at home and I think they have big expectations in the Champions League this season.
"What happened last season (with the second-round exit to Real Madrid), that can't be the same, so I think he is more under pressure."
Hyypia backed the former Everton manager to succeed with United but hoped that it wasn't against Leverkusen.
"I think David Moyes is an experienced manager and I think that everyone should give him a little bit more time to get things running," Hyypia said.
"Hopefully it doesn't happen tomorrow that they get things running and we can give them enough problems that they can't get their rhythm in the game."
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.