Campbell won two Premier League titles with the Gunners alongside the likes of Patrick Vieira, Tony Adams and more, but the club's wait for the top prize in English football looks set to extend to 13 years after their 3-1 defeat to Chelsea on Saturday left them 12 points behind the leaders.
The former England international questioned whether Arsenal have the character required to win the league nowadays, and believes that they now face a fight to keep hold of their place in the top four this season.
"I don't know what's happening now, but when I was there we used to police it ourselves. We had the characters to police it ourselves. We didn't allow the whole 45 minutes to go by, we would address it on the pitch because if you wait for 45 minutes and you are in, you might be 2-0 down," he told Sky Sports News.
"And we had the characters you know would say something, Patrick would say something, Tony, Martin Keown, David Seaman, all these guys, from the front Thierry [Henry], Dennis Bergkamp, all these guys would chip in on the pitch while the game was going on. That's the key, you've got to have those characters on the pitch. The guys who will say something on the pitch, you don't need one, you need almost four or five saying their stuff if things are not going right.
"I think with Arsene [Wenger] I think he believes he can win the league. I think he starts every season saying, 'right, we can win the league playing this style of football'. Obviously reality kicks in halfway through the season. It's not that easy because you need the personnel on the pitch. And also even in the stands and the bench, you need guys who can come on and make that impact and make the difference or are hungry or fighting to get on to the pitch, so when they do get on the pitch they are ready. I think it's the balance.
"Top four, if they keep going like that, is going to be extremely hard to get because you've got Man United who are motoring now. Maybe they might just scrape it. Man United might run out of games. The might get that fourth spot, Arsenal."
Arsenal, who now sit fourth in the table, will look to recover from back-to-back defeats when they host a resurgent Hull City on Saturday.