The Gunners are still in the frame for this season's Premiership.
"Winning the first one is not easy," Campbell told the Sunday Times. "You've got to go for the League Cup, the FA Cup, all competitions, because you never know which one is going to come your way. But it's all about winning something, going for it every year with all guns blazing.
"We've got to keep pushing for the league. That's the only thing we've got now. We have to win every game. We've had a little bit of a break to recover and there will definitely be a couple of twists in the race yet, hopefully in favour of us."