Arsene Wenger's men followed up their 6-0 drubbing at the hands of Chelsea with a 2-2 draw at home to Swansea City on Tuesday, a result that leaves them six points adrift of the Premier League leaders.
A return of just eight points from seven matches has seen Arsenal slip to the periphery of the title race, while even a top-four finish is now under threat as a result of Everton's four-match winning streak.
Campbell, speaking after the release of his book, Sol Campbell - The Authorised Biography, feels the defeat to Chelsea was the hammer blow to Arsenal's hopes.
"If that result was different they could still be in the race, I think that result kind of puts them definitely out of the race," the former Arsenal defender told Perform.
"A miracle has to happen (for Arsenal to win the league), for the other teams to lose games, for them to win games, for it to all change around.
"Mathematically it's still there (but) the whole momentum of them trying to get back into winning the Premier League has definitely been dented and I think it could be gone now."
Campbell, who lifted the two Premier League titles and three FA Cups during his time with Arsenal, believes that Wenger will have been badly affected by the recent dip in form and says the FA Cup must now be a priority for his former club.
"I think he (Wenger) will be definitely hurt," he added. "It's a special time when you get a thousand games and you always want to end in a happy way or have a good result. Obviously that didn't happen so I'm very, very disappointed and he'll be deeply hurt.
"I think he'd like to end with a win under his belt this season.
"I think definitely the FA Cup is the only thing to really, really go for and they can't miss that chance because it's a special cup and I hope the players treat it as a special cup, and respect the team they're playing against (Wigan Athletic) because that's the beauty of the cup; if you disrespect it, it can really turn around."
