Cole now expects the champions to put a run together and get the defence of their title back on track.
"Well hopefully [the win] will have a positive effect. Hopefully, from now until the end of the season, we can get the steam going and win as many games as possible," he told the club's official website.
"The championship is so open this season, it is unbelievable how many teams could win it and how many teams have not actually grasped the opportunity when another team slips up. We did it on Sunday, but the others haven't."
Cole spent six years as a player with United, winning five Premier League titles, two FA Cups and the Champions League before his departure in 2001.