The Uruguayan striker was given a four-month ban from football, and a nine-game international suspension by FIFA last month after he bit Italy defender Giorgio Chiellini during a World Cup group game.
Suarez, who was a Liverpool player at the time of the offence, has since completed a £75 million switch to the La Liga side, but will not be able to play until the end of October.
However, Barca are still trying to reduce the length of the sanction and the new boss has said that while they are hoping to see the ban lessened, it would be "no tragedy" if they had to play the first few months of their campaign without Suarez.
He told the club's official website: “Ideally, we’d have all of the players from the very first day, but we knew what the situation was when we signed him. We’re still hoping the suspension can be changed, but it would be no tragedy is it wasn’t.
"You must remember that we’ve got plenty of other players. There’s a long season ahead and there will be chances for everyone. So it’s no excuse that he’s suspended."
Enrique also enthused about the prospect of having Suarez teaming up with Lionel Messi and Neymar in what would arguably be the finest frontline in world football.
"Coaches always want the best footballers, and we have them," he added. "I’m delighted, but it won’t just be those three playing. There are lots of players who can form part of the attack, and to be a good team you need everyone to chip in."
Suarez moves to Barca after an outstanding season with the Reds.
The forward scored 31 goals for Brendan Rodgers' side en route to winning the PFA and FWA Footballer of the Year awards.