The Reds missed out on the latest European drama after being knocked out in the round of 16 by Atletico Madrid. Los Rojiblancos hosted Manchester City on Wednesday, with the English side prevailing after an intense encounter, and the night before, Real Madrid triumphed over Chelsea in a breathtaking tie at the Santiago Bernabeu.
United managed a draw at Atletico's Wanda Metropolitano in February, but were eliminated after losing at Old Trafford in the second leg.
Rangnick wants the players to use their quarter-final absence as motivation in the final seven games of the domestic campaign, with a place in next season's Champions League remaining the key incentive.