The Russian billionaire is currently celebrating his 10th anniversary at Stamford Bridge after buying the club from Ken Bates.
Despite enjoying success on the pitch at the time, Lampard has revealed that the Blues were struggling behind the scenes.
"During that season, I remember talk about how we had to make cut backs; in the canteen, by not staying in hotels the night before home games, things like that," the England international told Chelsea's official website. "We were aware that there were a few troubles at the club.
"At Chelsea we were still a big club and we were doing pretty well but things weren't so good behind the scenes by the sounds of it. We were made aware of that as players."
Chelsea have gone on to win 11 trophies since Abramovich completed his takeover 10 years ago.