The Manchester City forward compared the jobs given to Lampard and Rangers manager Steven Gerrard with the roles landed by Sol Campbell and Ashley Cole.
Campbell is currently the manager of Southend, having spent nine months at Macclesfield, where he helped the club avoid relegation from League Two. Cole, meanwhile, is on staff at Chelsea's academy and coached at Derby under Lampard.
Lampard, in response to Sterling, said that he felt the 25-year-old's comments were "slightly wrong" and that the comparison he was making was "very casual".
"I think in the actual case of managers, I think he got it, from my point of view, slightly wrong," Lampard said.
"Those opportunities have to be equal for everybody, I think we all agree on that. But within that then there are the details of how hard you worked.
Frank Lampard and Raheem Sterling
Image credit: PA Sport
"I certainly worked from the start of my career to try to get this opportunity, and there's a million things along the way that knock you, set you back, that you fight against."
"The FA do a lot of good work, I've just finished my pro licence, it was very diverse, it was very open," he added. "That needs to be encouraged.
"If there's anything we can do to ensure everyone gets an equal opportunity in the paths towards management then it needs to be done - and the numbers suggest that needs to be done.
But with Raheem, the individual comparison, when you don't have the detail of each person's pathway, I felt that wasn't quite right.
"And again I'll level that out slightly, because I want to say that Raheem Sterling as a player and as a person and what he's stood up for over the last two years, I think has been fantastic."
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Southgate offers different view
In contrast to Lampard's views, speaking earlier this month England manager Gareth Southgate agreed with Sterling and even admitted he was not qualified to manage when he was appointed Middlesbrough boss in 2006, aged 35 and unqualified as a coach.
"I’m better educated now in this area (of white privilege),” he told The Times. “I know I got an opportunity at Middlesbrough when I wasn’t qualified.
"That came because I’d worked at the club and the owner knew me. I couldn’t say that opportunity would have been there for somebody else."
Premier League players have shown their support on the Black Lives Matter issue by taking a knee moments before kick-off in fixtures, while protests have been held around the world as part of the movement following the death of Floyd in Minneapolis on 25 May.
City, featuring Sterling, will take on Lampard's Chelsea on Thursday evening. If City do not win the match, Liverpool will be declared Premier League champions.