The pair battled it out for more than four-and-a-half hours in a five-set thriller, with Tsitsipas eventually prevailing 2-6 7-6 3-6 6-3 6-4 to advance to the second round at Flushing Meadows.
However, Murray was disappointed with how much time his opponent spent off court; Tsitsipas took two bathroom breaks of longer than seven minutes and also received a medical time out.
“It’s just disappointing because I feel it influenced the outcome of the match,” Murray told reports after the match. “I’m not saying I necessarily win that match, for sure, but it had influence on what was happening after those breaks.
“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.”
Tsitsipas, who didn’t break any rules, took lengthy toilet breaks at the end of the second and fourth sets and received a medical time out for an apparent foot injury before the fourth set.
Murray could be heard complaining to chair umpire Nico Helwerth and US Open match supervisor Gerry Armstrong about the amount of time Tsitsipas was taking.
The Scot said he told his team before the match to “expect” that from his opponent “if things weren’t going his way” and revealed there have been discussions about changing the rules to prevent those lengthy stoppages from happening.
“Ultimately, they [the officials] can’t do anything because the rules are there,” Murray said. “But I sit on the player council and we speak about it all of the time, about changing these rules, trying to make it less easy for the rules to be exploited, I guess.
“Some suggestions are if you take a medical timeout or a break before, let’s say, my serve, that you forfeit the game. I just start the set one-love up. That’s one thing that’s sort of been discussed. A couple of other things are, like, you get two five-minute breaks during a match or something — and that’s it. There’s various different suggestions that are out there.
“That’s what I feel, but if everyone else feels like that’s totally cool and there’s no issue with it, then maybe I’m the one being unreasonable, but I think it’s nonsense — and he knows it, as well.”
After the match, Tsitsipas insisted he had done nothing wrong and that he had no hard feelings towards Murray.
“If there’s something that he has to tell me, we should speak the two of us to kind of understand what went wrong,” he told reporters. “I don’t think I broke any rules. I played by the guidelines, how everything is. Yeah, definitely something for both of us to kind of chat about and make sure.
“I don’t know how my opponent feels when I’m out there playing the match. It’s not really my priority. As far as I’m playing by the rules and sticking to what the ATP says is fair, then the rest is fine. I have nothing against him. Absolutely nothing.”
Tsitsipas, who is chasing his first grand slam title, went on to explain why he took so much time during those bathroom breaks.
“Well, I think it’s clear that I took my clothes with me when I left the court,” he said. “That’s the amount of time it takes for me to change my clothes and to walk back to the court takes a little bit of time.
“I don’t know what’s the rule regarding that, if there is one. But, as far as I know, you’re allowed to have two toilet breaks to go change your clothes in a five-setter and one in a three-setter.
“I followed that throughout my entire career. I’ve never broken any rules, so I see no reason that that’s a problem anyways.”
Elsewhere, defending women’s singles champion Naomi Osaka eased through her opening round match with a straight sets victory over Marie Bouzkova.
In her first grand slam appearance since withdrawing from the French Open back in June, Osaka was pushed hard in the first set by her Czech opponent, before comfortably closing out the match 6-4 6-1 to advance to the second round.