Slot has made an impressive start to life at Anfield despite the difficult task of replacing Jurgen Klopp.
Luis Diaz struck twice before Mohamed Salah sealed the victory at Old Trafford, making it three straight wins for the Reds.
Netherlands boss Ronald Koeman watched the game with a number of Dutch players included, and ahead of their upcoming Nations League fixtures, he explained why he felt Slot is 'lucky'.
Koeman said: 'I watched because of the many Dutch players. But of course I also looked at it from a manager's point of view.
Koeman said Slot is lucky to have the front three that he has at his disposal after Mohamed Salah, Luis Diaz and Diogo Jota all starred for the Reds during the victory over their rivals
'Arne Slot is doing a slightly better job. But if you have the front three that he has, you must realise you are lucky.'
The new Liverpool manager has walked into a side that boasts an impressive array of attacking talent.
Liverpool have one of the best attacking players in the world in the form of Salah, while he played alongside Diaz and Jota against the Red Devils.
Dutch international Cody Gakpo and Darwin Nunez were on the bench, while the Reds have also recently signed Federico Chiesa from Juventus.
Ten Hag meanwhile is under pressure after only just keeping his job at the end of last season.
United finished eighth in the Premier League and were knocked out of the Champions League at the group stage, though he kept his job because of their FA Cup victory.
However, the Red Devils have got off to a slow start this season with two defeats from their opening three games.
As well as Gakpo, Virgil van Dijk, Ryan Gravenberch, Joshua Zirkzee and Matthis de Ligt all featured during the game.
Gravenberch impressed in midfield for the Reds, though Koeman took a fierce dig at the 22-year-old in his press conference.
The former Everton and Southampton boss responded to one journalist's glowing praise for the defensive midfielder by saying: 'I am glad you added that last part. I have always seen the potential in him.
But I believed he lacked focus, this is something that he had to improve and now it seems that he finally realises what is asked of him.'
Despite turning out 26 times for the Reds last season, Gravenberch did not play a single minute in a Euro 2024 campaign which saw the Netherlands reach the semi-finals.