Lampard, who at 33 is just a a year younger than the boss, has lost his automatic starting place in the line-up and was on the bench for the 3-1 Champions League defeat at Napoli last week.
He also started as a substitute in the FA Cup match against Birmingham City last weekend.
After returning to the starting line-up and scoring his 150th career league goal in Chelsea's 3-0 win over Bolton Wanderers on Saturday, Lampard stressed his commitment to the club but recognised strains with the manager.
Asked about their relationship, he said: "I think, from the outside, you can probably see that it's not been ideal but the important thing is not to focus on individual relationships too much.
"It can only be negative and people do like to play on negatives."
Although Villas-Boas praised Lampard after Chelsea ended a run of five matches without a win, he said his display still did not assure him of a place in the team.
"There have been certain issues," Lampard said. "Certain players, we don't like not to play. But it's never a case of players throwing their toys out of the pram to the detriment of the club.
"The only way we can push on from now and secure Champions League football next year, potentially move through in the FA Cup and the Champions League this year, is to be positive.
"It's in the club's interest. It's not about any one individual here and negative things can take the shine off it."
Villas-Boas said Lampard's performance was "fantastic" but added: "There are six players competing for those three positions in midfield. When we play with a number 10, it's even less. It's six players for two.
"Frank had a big, big day and it was important for him after the disappointment of coming out of the team against Napoli and Birmingham.
"He proved he can make the difference for the team. We always pick the team we think is best for the game and today he showed why he is one of the best.
"You [journalists] asked me directly at Napoli if Lamps was disappointed at missing the game and I assure you that he was, just like Raul [Meireles] was disappointed today - just like Oriol Romeu and John Obi Mikel."
Asked if Lampard would start against West Bromwich Albion next week, Villas-Boas replied: "That is not the way it works."
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