The Spanish outfit reached the final of the competition last season and have once again been tipped to advance deep into the tournament.
However, Suarez is under no illusions as to the size of the task in their group opener in Greece.
"Playing in the Champions League is always special, every player in the world wants to play in it. We couldn't win the final last year, but what's done is done and it's in the past. We learned what we needed to improve. We know that tomorrow will be a difficult match and we're very motivated," Inside Spanish Football quotes the midfielder as saying.
"We know that this is the best club competition in the world and in order to win we need to give 120%. Olympiacos are a very difficult opponent and we must play with humility. We're up for the fight.
"We had a great campaign last year and a lot of what we saw and learned last year will serve us well this season. But right now we need to focus on this match here against a difficult opponent who beat [Manchester] United last season. We're playing with the same humility and focus that we always have."
Olympiacos reached the last-16 stage last season before losing to Manchester United.