The result extended the Premier League champions' worst run since 2014 and left the Dutchman searching for answers ahead of a crucial Champions League trip to Eintracht Frankfurt on Wednesday night.
Liverpool, who had already fallen to Crystal Palace, Galatasaray, and Chelsea before the international break, appeared on course for a point when Cody Gakpo cancelled out Bryan Mbeumo's opener. But Harry Maguire's 84th-minute header sealed a dramatic win for United and deepened the Reds' growing crisis.
Slot admitted the run represented one of the sternest tests of his managerial career since replacing Jurgen Klopp in the summer. "I think as a manager you constantly face challenges," he said. "When you start, you need to win games. Then you move to a bigger club, and people ask how you will cope.
"Being Klopp's successor was called the biggest challenge of my career, and now losing four in a row is another challenge. The life of a football manager is an ongoing challenge."
Despite the poor results, Slot insisted Liverpool's performances had not been without positives. "Of course concerns if you lose four times in a row. You have to be concerned because you know how it works in football," he added. "If we can keep making performances like this we will have a good chance of winning a game of football.
"We came back and if that mentality is there there's a lot to take into upcoming games."
He emphasized the chances created, noting: "People tend to forget how many chances we had. Cody Gakpo hitting the post twice. Already in the first half we had chances to go 1-1, but in the second half we had more chances because the other team gets tired."
The Dutchman also admitted Liverpool's attacking approach had left them vulnerable at the back, particularly from set-pieces. "And when you take into account that we did not concede. We had to defend a set piece and like against Palace we concede on a set piece," Slot explained.
"And that's hard to take because it is very difficult to win a game of football if you have a negative balance on set pieces. Of course we concede one or two extra chances because of the risk you take when you're 1-0 down."
Liverpool will now look to halt their losing streak in Frankfurt before returning to Premier League action against Brentford at the weekend.
Manchester United defender Matthijs De Ligt has revealed that the team specifically targeted Liverpool's full-backs during their 2-1 win at Anfield on Sunday, exploiting what they saw as a key vulnerability.
Mikel Arteta has insisted he remains "very happy" with Eberechi Eze, despite the midfielder's inconsistent form since joining Arsenal.
Micah Richards has branded Nottingham Forest's decision to sack Ange Postecoglou after just 39 days in charge as "ridiculous", warning that the club's impatience could set a dangerous precedent in football.
Thomas Frank has admitted that Tottenham's ongoing struggles at home are proving difficult to fix after their 2-1 defeat to Aston Villa extended a worrying run of poor results in north London.
