The Gunners were held to a 0-0 draw by the Italian side in Thursday's (19.09.24) fixture and the midfielder was frustrated that his team had to settle with a point.
Rice told TNT Sports: "It’s tough to win away in the Champions League, really tough.
"These are European [UEFA Europa League] champions. They’ve had the same manager for nine years, playing man-to-man [marking] all over the pitch."
Arsenal were indebted to goalkeeper David Raya who superbly saved Mateo Retegui's penalty and rebound but Rice felt that the result was an opportunity missed with tough games to come in the expanded European competition.
He said: "It’s a good point to start. Obviously, we want to win every game. That’s the ambition of the players, the manager, the club. But we’ve got really tough games coming, that’s the format.
"You have to win every game. We’ve got PSG at home, which will be a great game.
"We’ll take one game at a time. We’ll go back to the Prem now, but we’ve got our sights on the Champions League because we’ve got the players to do it.
"We are delighted with another clean sheet, the two centre-halves I can’t speak highly enough of them. The keeper has gone to the next level, unbelievable.
"They love defending and when you have a little triangle like that who want it as much as they do it’s really good. But we are all gutted in there because we want to win."