Reports suggested the forward had been sidelined by Bielsa after angering the head coach during their 1-0 defeat to Monaco last weekend.
Payet's absence from Sunday's 2-1 win over Lille added further weight to the idea that the Argentine coach was punishing the 27-year-old.
However, Bielsa denied there had any problems between the pair and said leaving Payet, who has scored five league goals, out had been purely a selection choice.
"There has been nothing in particular, I just decided choose another player for the game today," said Bielsa. "And I found that it was not necessary for him to be present in the 18 players called.
"Today's decision is not a penalty because a sanction shows a lack of discipline, and there was no breach of this kind.
"Payet is an outstanding player, one of the best in the team overall."
Sunday's victory ensured Marseille finished the first half of the season top of the table by three points from defending champions Paris Saint-Germain.
They return to league action on January 9 against Montpellier.
‘He instantly popped into our ratings as one of the best U21 midfielders in Europe. The impressive thing is Slot has made him into more of a no.6' Inside Ryan Gravenberch's transformation at Liverpool
‘I don’t think Liverpool would look at Ollie Watkins, a striker isn’t a pressing issue for them – it’s Arsenal who need one’ Former Reds star explains why his old club don’t need an out-and-out forward this summer
