The former Blues midfielder says the club should have backed Frank Lampard by bringing in reinforcements during the winter window
Serge Gnabry scored twice and Robert Lewandowski added a goal of his own as Chelsea were undone at Stamford Bridge.
The loss comes on the heels of a quiet January, as Chelsea failed to bring in any new signings despite seeing the club’s FIFA-imposed transfer ban halved on appeal.
Frank Lampard’s side has struggled in recent weeks, with the Blues having won just one of their last five Premier League matches.
And Cole says those struggles come as a result of the club’s inability to bring in any new faces during the January window, leaving the club shorthanded for matches like Tuesday’s.
“I think knowing this game was on the horizon, Frank would have been desperate to get players through the door,” Cole said on BT Sport.
“You’ve asked [Olivier] Giroud, who’s done brilliant for you at the weekend, he’s not been fit and a 32-year-old striker to come and lead the line against probably one of the best sides in Europe at the moment, it just looked like he ran out of steam towards the end.
“So not recruiting has definitely affected the performance and the team.
“Bayern Munich were sublime from start to finish. We talked about the patterns of play, the passing, they just really drilled Chelsea tonight and it’s a momentous task for them going to Germany.”
While Chelsea’s lack of depth was on display, Bayern’s quality was also a key factor in Tuesday’s victory.
Rio Ferdinand added that Hansi Flick’s Bayern team deserves praise for their performance, which moved them one step closer to the quarter-finals.
“An absolute education, it was a clinic put on by this Bayern team,” Ferdinand said.
“They never really got out of second gear, they didn’t need to, they upped it every now and then.
“Gnabry didn’t even feature really in the first half, comes out second half explosive, scores two exquisite goals. They just showed they had that quality, especially in the top end of the pitch.
“The two midfielders [Joshua] Kimmich and Thiago controlled the game, controlled the tempo of the game, and when the ball got into the final third at the right times these boys were clinical, as they’ve been throughout the season in Germany.”