It comes after third seed Tsitsipas took a number of lengthy toilet breaks during their US Open match- when Murray could be heard accusing his opponent of "cheating".
The British number 1 seemed particularly angered by the Greek player taking an eight-minute break before the fifth set of their first round match which Murray lost.
Tsitsipas, 23, then went on to win the decider as he sealed a 2-6 7-6 (9-7) 3-6 6-3 6-4 victory.
And Murray, 34, was keen to stress it isn't simply "sour grapes" as he'd have said the same even if he'd won.
He said: "It's not so much leaving the court.
"It's the amount of time.
"It's nonsense and he knows it."
"That's annoying for me because it sounds like sour grapes because you've lost a match.
"I would have said the same thing if I'd won, I promise."
"It's just disappointing because I feel it influenced the outcome of the match.
"I'm not saying I necessarily win that match, for sure, but it had influence on what was happening after those breaks."
Tsitipas didn't actually break any rules, but also left the court for a bathroom break at the end of the second set, as well as having a medical time-out for treatment on a foot injury before the beginning of the fourth set.
During the match a clearly irate Murray could be heard shouting: "It is cheating", before also complaining to umpire Nico Helwerth and the match supervisor Gerry Armstrong about the conduct of his opponent.
He said to Armstrong: "It's never taken me that long to go to the bathroom ever."
Continuing with his past-match comments Murray added: "Every single time it was before my serve, as well.
"Also in the fourth set when I had 0-30, he chose to go and I think he changed his racquet.
"It can't be coincidence that it's happening at those moments.
"I rate him a lot.
"I think he's a brilliant player.
"I think he's great for the game.
"But I have zero time for that stuff at all, and I lost respect for him."