The Europa League is now their best chance of securing Champions League football next season - Thursday's semi-final second leg against Celta Vigo awaits, with Mourinho claiming it is now "impossible" for United to finish in the top four.
As a outcome, and with knowledge their opponents will have seven more days rest before the Stockholm final, Mourinho will field different lineups in their forthcoming games.
'But if we are, I am (still) going to rest players.
'The boys gave everything they had, I'm really pleased for them. I left Highbury, they were crying, I left Emirates, they were crying. And I don't have another solution.
Indeed, with Arsenal four points clear in fifth and Everton unable to catch Mourinho's charges, sixth place looks nearly inevitable for a team that has occupied that position for nearly the entire campaign.
"We put players back in the right positions". So that's the game. We gave a hard match to our opponent. We got no injuries.
"And because we go with everything on Thursday and we cannot go with everything against Tottenham". But the match on Sunday is important for us, too.
United boss Jose Mourinho has already selected the goalkeeper to start ahead of final clash with Ajax as he has two world-class stoppers to choose from.
Marouane Fellaini will also miss out as he serves the final part of his three-match domestic suspension. "And hopefully nobody will complain because we have a final three days later".
Keane also questioned the role of United skipper Wayne Rooney, who has struggled for playing time this season.
As mentioned by the decorated Portuguese manager, the victor secures a Champions League berth, an incentive that was introduced at the beginning of the 2015/16 competition which Sevilla won.