Manchester United lost 1-0 to Everton in the Premier League at Goodison Park to put a dent on their Champions League prospects.
The Red Devils now find themselves in seventh position, six points behind Tottenham Hotspurs, who occupy the final Champions League spot.
United faced an Everton side low on confidence and battling to retain their Premier League status but they did not do enough to claim the needed three points.
Manchester United now have just one win in their last five league matches.
"If we play like we did here we just don't deserve it," Rangnick said after the game.
"The players themselves should be eager to play international football, if possible Champions League. In order to qualify for Europe you have to be able to score in 95 minutes in a game like this."
"With all respect to Everton - because they have a good team - but if you don't score against a team who conceded three goals against Burnley, you cannot expect to get anything out of it," he added.
"The first 25 minutes we were in full control of the game. We didn't even in those 25 minutes take enough advantage out of that dominating period.
"You could literally feel that Everton were crumbling after that result against Burnley. They were quite logically not full of confidence but we didn't take advantage of that."
Rangnick does not believe the uncertainty around Manchester United's next manager should be used as an excuse for the drop in form.
"I don't think this should be an excuse," Rangnick told BT Sport.
"We are Manchester United. We have lots of international players. There shouldn't be an alibi.
"There will be a new manager next season. If this is announced now or in 10 days it shouldn't have an impact."
