Pressure continued to mount on Arsene Wenger's side on Sunday as they were beaten 3-0 by Champions League-chasing Everton.
Goals from Steven Naismith and Romelu Lukaku set Everton rolling at Goodison Park, before former Blue Mikel Arteta's own goal completed the haul.
Roberto Martinez's side are now just one point behind Arsenal, with a game in hand, as the fight for the final Champions League spot rumbles on.
Speaking to Sky Sports News Radio Campbell said: "Too many times now Arsenal have gone away from home and not performed.
"It's not rocket science now. There's just a lack of toughness, there's a lack of belief in the squad and it shows on the pitch.
"The manager doesn't set the players up to lose. You have to look at the players."
Arsenal have registered just four points in their last six matches away from the Emirates and Campbell believes Saturday's FA Cup showdown with Wigan at Wembley is a must-win clash.
"That confidence you need, Arsenal just don't have it," he claimed.
"We've seen it far too many times, against big teams they just capitulate and this is simply not good enough.
"Arsenal have to win or it's a catastrophe season. It's great starting well but it's not how you start, but how you finish."
Campbell, who went on to represent Everton after his time at Highbury, believes Arsenal failed to show on Sunday but claims the Toffees deserve the plaudits.
"I thought Arsenal would turn up but Everton were just fantastic I thought yesterday," he said.
"They just didn't let Arsenal into the game at any stage. It was just one-way traffic, Arsenal were steamrollered."
Everton have six games remaining, including fixtures with Manchester City and Manchester United, and Campbell expects his former side could well usurp Arsenal and clinch a Champions League place.
"I think they can," he said. "It's going to be very difficult because of the run-ins, Everton probably have the harder run-in playing some of the teams going for the title.
"But the way Everton are going at the minute, teams are not going to be happy going to Goodison Park.
"They're playing free, they have a game-plan and everybody knows what they're doing. They're playing with a confidence I have never seen at Everton for a long, long time."
The impact of Martinez since his arrival in the summer following the departure of David Moyes has been documented by many and Campbell believes achieving Champions League qualification would round off a dream year for the Spaniard.
"You've got to give credit to the manager," he added. "It's virtually the same players that were there under Moyes but they're excelling in the way he wants them to play.
"David Moyes did a fantastic job at Everton but I think Roberto Martinez has taken them on to another level.
"I think the Champions League means everything to a club like Everton. It's been a long time since Everton rubbed shoulders with the best."