The Liverpool right-back, having been heavily linked with Real Madrid this week, had a game to forget as United frustrated the Premier League leaders with a battling display at Anfield on Sunday.
Alexander-Arnold, now in the final six months of his contract at his boyhood club, struggled to impose himself and was at fault for the visitors' first goal.
Reds manager Slot does not believe the speculation had a big impact, but accepts other people will view the matter differently.
The Dutchman said: "I think nine out of 10 people will tell you that it affected him. I'm (the) one of the 10 that tells you that I don't think that affected him.
"What affected him is that he had to play against Bruno Fernandes and Diogo Dalot, two starters for Portugal, great, great players.
"If these players set themselves to a game - and that is what United once in a while does - then it's very difficult to play against them.
"I think that is more difficult for Trent to play against than the rumours that were there during the week.
"But that's my opinion, and probably everybody's going to tell you that it had to do with the rumours."
Liverpool, who restored a six-point lead over second-placed Arsenal with a game in hand, fought back to lead with a Cody Gakpo strike and Mohamed Salah penalty after Martinez fired United ahead.
Yet they lacked their usual control and United, showing a spirit they have conspicuously lacked of late, restored parity 10 minutes from time through Amad Diallo.
Things might even have got worse for Liverpool as Harry Maguire spurned a gilt-edged stoppage time chance to snatch victory for United.
Slot said: "Of course it feels for us as two points dropped.
"I think for many people what stays in their head is what happens in the end and that was a big chance for Maguire, of course.
"But what you then might tend to forget is that two minutes before, Virgil (van Dijk) had just as big a chance to make it 3-2 for us."
United's performance arrested their run of three successive defeats and captain Bruno Fernandes voiced his frustration the side could not produce such intensity consistently.
The Portuguese told Sky Sports: "I'm pretty upset because if we show this today at Anfield against Liverpool, who are first in the league and probably the outstanding team in the Premier League this season, why can't we do this every week?"
Manager Ruben Amorim was pleased with the response of his players after strong criticism following Monday's loss to Newcastle.
He said: "I want to see my team play so much better but I think the most important thing here is the mentality. That is the key for everything."
