The Gunners once again came up short against the Blues as they were out-muscled 3-0 at Emirates Stadium on Sunday, with Didier Drogba scoring a brace.
Rosicky, who was also sent on during the second half to try to turn Gunners fortunes around, believes the immediate response from the team - with a midweek trip to Manchester City in the Carling Cup and then Stoke the visitors to Emirates Stadium - will be key to ensuring they can yet salvage a campaign which had started full of promise.
"The next match is vital," the Czech midfielder said.
"After a defeat like this, you need to have a good reaction, if not it will be even more difficult.
"It will be very tough to win the title now, we know that, but [to let the season fall apart now] would be the biggest mistake we can make.
"The only thing you can do is carry on and try your best again."
Rosicky added: "It is difficult with Robin out, but I thought this game was the chance for other players to step in.
"We tried to play our usual football against Chelsea, but they defended very well and in the final third we produced almost nothing - that was the main reason we lost."
"If Chelsea continue to play like that, then it will be difficult for anyone to stop them," he added.
"But everything can still happen - they will lose some players to the African Nations Cup, and could get some injuries."