Ten Hag was axed by United on Monday after a little over two years in charge following a disappointing start to the season, with United down in 14th in the Premier League and yet to register a win in Europe.
Slot only arrived in England this summer, but played his part in Ten Hag's downfall as he led his Liverpool side to a 3-0 win at Old Trafford last month.
Despite the rivalry that exists between Liverpool and United, Slot has offered some sympathy for Ten Hag's situation, and has tipped his fellow Dutchman to bounce back.
'He's a Dutch manager which makes it even harder for me, for us as Dutch people,' Slot said at a press conference ahead of Liverpool's trip to Brighton for their Carabao Cup tie on Wednesday.
Arne Slot has expressed sympathy with Erik Ten Hag following his Man United sacking
'Always your first thoughts are with the person. We are all in this job so we know it can happen, but if it happens, especially because I know him a little bit and I know how much work he puts into it, then to get this news for him is a pity.
'But we also know, especially coming from Holland, how well he did at Ajax and that he won two trophies over here so we will see him in the near future somewhere at a big club again. At this moment, for him and his family it's a big disappointment.'
Prior to his arrival at Anfield, Ten Hag had appeared to aim a jibe at Slot back in May when he downplayed Feyenoord's achievements last season.
Feyenoord finished seven points behind champions PSV Eindhoven, and Ten Hag told Voetbal International: 'People have been going overly lyrical about Feyenoord.
'Feyenoord were steady this year, but not top. PSV Eindhoven were two classes better in all areas. In terms of dominating the ball, in terms of putting pressure, in terms of intensity, you name it.'
He added: 'PSV Eindhoven were better than the rest by such a long distance, even so much better than Feyenoord.'
But Slot gained his revenge earlier this season as Liverpool eased past United, and he has now outlasted Ten Hag in England.
United have moved swiftly to find Ten Hag's replacement, with the Red Devils edging nearer to appointing Sporting Lisbon manager Ruben Amorim.
Meanwhile, Ten Hag boarded a plane back to the Netherlands on Monday where he is set to spend some time with his family after being relieved of his duties at United.