The 26-year-old unsurprisingly started the contest on the right-hand side of the Liverpool backline and witnessed Darwin Nunez finish off a blistering counter-attack to put the hosts ahead inside the first 20 minutes.
However, just a couple of moments later, Alexander-Arnold was seen sitting on the turf with an unknown problem, one that was serious enough to take him off the pitch as Conor Bradley took his place.
Slot briefly spoke to Alexander-Arnold before the right-back trudged down the tunnel with the medical team, but Bradley did a competent job on the right-hand side for the remainder of the match.
The Reds moved five points clear of Manchester City at the summit of the Premier League standings by sinking Unai Emery's side, but concern quickly turned to Alexander-Arnold's condition ahead of some key fixtures.
Slot expects Alexander-Arnold to miss England matches
Liverpool return from the international break with a trip to Southampton on November 24, three days before Slot's side host Real Madrid - Alexander-Arnold's reported admirers - in the Champions League.
Speaking to the media in his post-game press conference, Slot admitted that he was still in the dark about the severity of the defender's problem, but he is not expecting him to be able to play in England's Nations League matches against Greece and the Republic of Ireland later this month.
"It's difficult to say how serious it is, but it's always serious if a player goes out in the first half. Not because I didn't like him, but because he asked for it himself," Slot told journalists.
"He didn't ask for it because he was tired, he asked for it because he felt something. That's first of all not a good sign, but it is always difficult so close after the game to tell you exactly what it is.
"Let's wait and see. I would be surprised if we will see him playing for the England national team this week, but hopefully he can."
Who could replace Alexander-Arnold against Real Madrid?
It is very early days in Alexander-Arnold's latest injury blow, but the Liverpool coaching team will no doubt be drawing up contingency plans in case their vice-captain is unable to face Los Blancos in just under three weeks' time.
Bradley is Alexander-Arnold's natural understudy and proved during Jurgen Klopp's final season that he is more than capable of going toe-to-toe with the big boys, although he is yet to face the Vinicius Junior test.
Should Slot decide that a more experienced head is required to deal with the player who finished second in the 2024 Ballon d'Or voting, Joe Gomez is another option, having made cameo appearances on the right against AC Milan and Chelsea already this season.
Liverpool were also missing Alisson Becker, Harvey Elliott, Federico Chiesa and Diogo Jota for the win over Villa, but the former three may all be back in time to face Carlo Ancelotti's team on November 27.
Once that encounter is done and dusted, Liverpool kick off the advent season with another blockbuster battle, hosting Manchester City in the Premier League on December 1.