The Brazilian centre-back thought the Portuguese tactician should have treated the Stamford Bridge favourite better and that his reputation at Chelsea deserved to be protected more carefully.
The former Porto boss took over in last summer and had an up and down relationship with Lampard, which culminated in him openly admitting the player had criticised him before the defeat to Napoli a fortnight ago.
"Andre is not the kind of person who talks a lot, he's someone who is a bit closed. That's just the way he is,” Alex told O Jogo.
“I saw some comments of Lampard recently and I think he deserved more respect.
“It is true that a player knows he will sometimes have to stay on the bench, especially after reaching a certain age. That's not a problem.
“But with Lampard's history at the club, where he has more than 10 years, he deserves a word or an explanation from the manager.
“Fundamentally, it was a question of respect for everything that he represents for Chelsea.”
Villas-Boas’ time was up at Stamford Bridge on Sunday when owner Roman Abramovich took the decision to relieve him of his duties after a lacklustre loss away to West Brom on the Saturday.
It appeared to be the straw that broke the camel’s back after a loss to Everton two weeks earlier sandwich the 3-1 reverse at Napoli in the Blues Champions League last-16 first leg.
Alex was one of the early casualties of the Villas-Boas reign when he was sent to train with the youth players with Nicolas Anelka after the pair had handed in transfer requests.
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