Lampard was sacked earlier in the season to make way for Thomas Tuchel, the German overseeing a remarkable turnaround in Chelsea's fortunes, guiding them to two major finals and steering them towards a top-four finish in the Premier League.
"I am friends with Frank and I've known him since I was a kid so you don't want to become a cheerleader," Cole told the Daily Mail.
"Tuchel has come in and done an unbelievable job but you can't disregard what Frank did - holding the fort during a difficult time, getting the club to a cup final last year, getting Champions League when they had lost their best player (Eden Hazard to Real Madrid in 2019).
"He brought in many of these young players in and put £200million of talent on the bottom line. They were going through a bad spell earlier in the season and that's Chelsea – you know if you go through a bad spell you could get the sack.
"Frank's fingerprints will be on this team but you have to credit Tuchel – to come in and have the impact he's had is extraordinary. Chelsea is in a really healthy place at the moment so I am very happy, very confident."