The former Liverpool skipper took over at the German outfit last term and finds himself making his Champions League debut opposite Moyes at Old Trafford tonight.
Hyypia is determined to inflict a defeat on Moyes, who has not enjoyed the smoothest of starts.
But even if Leverkusen extend a poor recent run of four home defeats in six European games at Old Trafford for the Red Devils, Hyypia is sure the Scot will eventually get it right.
"David Moyes is an experienced manager," said Hyypia. "Everyone should give him more time to get things running.
"Hopefully it doesn't happen against us. We have to stop them getting their rhythm and make sure they don't score in open play.
"Then we need to be very aware at set pieces."
Hyypia has already endured one of the best and worst days of his career at Old Trafford, that came six years apart.
"I was sent off after four minutes and watched the rest of the game in the dressing room," he said, of his 2003 experience. It was the only red card of my career and we lost 4-0.
"You remember those kinds of things but the first one that comes to my mind is playing my last game here, when we managed to win 4-1.