Goals from Mario Mandzukic, Thomas Muller and Arjen Robben cancelled out Patrice Evra's stunning opener to secure a 4-2 quarter-final aggregate win for Bayern Munich.
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"It's huge. United need to be in the Champions League," Jones told MUTV.
"Nights like this don’t come along too often. Teams like Bayern are who you want to be playing; if you want to test yourselves against the best you have to play them. In my eyes Bayern are the best.
United are unlikely to qualify for the competition next season for the first time since 1995-96 as they currently lie seven points off fourth-placed Arsenal, but Jones is eager to ensure any absence is short-lived.
He continued: "It's disappointing now, having gone out; you look back on the season and think that if we’d won such and such a game it might have been different.
"But we’ll keep fighting until the end of the season because nights like this might not come around too often and we want to make sure we are in them as much as possible."