Liverpool, who sit nine points behind the leaders Chelsea in ninth, have lost their last two games in Europe, and Meulensteen believes that the fault lies with Rodgers.
"Brendan Rodgers's biggest failure is that he's not invested in his staff," Meulensteen told BBC Sport.
"He has obviously got people around him who he obviously thinks are the right ones.
"But I think he could have done with someone who has been there, seen it and done it."
Meulensteen was a part of Sir Alex Ferguson's backroom staff between 2008 and 2013, helping United win several titles during his tenure as the first-team coach.