Saturday's 3-1 loss at Arsenal moved the fourth-set Gunners six focuses clear of United, who are 6th.
Weapons store have five games to play while United - looking for a third consecutive year in Europe's chief club rivalry - have four and look like passing up a major opportunity.
"As far as I might be concerned, even before the game it was not likely, yet after the present outcome it is gone, yes," said Rangnick.
Nuno Tavares' opener and a Bukayo Saka punishment put Arsenal 2-0 up, before Cristiano Ronaldo answered with his 100th Premier League objective.
Ronaldo arrives at 100 Premier League objectives - could you at any point name others to make it happen?
Bruno Fernandes squandered the opportunity of a merited balancer as he hauled a last part punishment against a post, before Granit Xhaka sentenced United to their second misfortune in five days.
'There are an entire heap of issues'
Joined experienced a 4-0 loss at Liverpool on Tuesday yet after two days the club reported that Erik ten Hag would turn into their next supervisor this late spring, with Rangnick set to move into a consultancy job.
Joined midfielder Scott McTominay told BT Sport: "There are an entire heap of issues as far as players, staff and everything higher up.
"However, for our purposes, when you return home and investigate the mirror, you can't be fulfilled surrendering three at Arsenal when we had the right to dominate the match.
"We had a half-good game today however the conviction, so large in football, it's only not there at the moment.
"The last four games are about pride for us. We need to complete too as we can do. At the point when the new mentor comes in we should be prepared for whatever might happen."
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