United sit four points outside Premier League top four in fifth position, but have a game in hand over Manchester City (four points ahead) and two over Liverpool (six points ahead) in the race for Champions League qualification.
While United can still secure a top-four finish, winning the Europa League represents another opportunity to secure Champions League football next season with the winners automatically qualifying for the elite competition.
The Red Devils face Anderlecht in Belgium tonight in the first lef of their Europa League quarter-final, with Mourinho regularly forced to balance priorities with a busy schedule in his first season at Old Trafford.
But with Antonio Conte's league leaders heading to Manchester on Sunday, Mourinho says he would face harsh criticism if he decided to rest key players against Chelsea.
"When it is still mathematically possible to finish in the top four I think if we play against Chelsea with our second team you would kill me," he said. The football country would kill me."
However, Mourinho hinted that while he will still fight for a spot in the top four, being in the Europa League will be vital if their domestic hopes fade.
"There is no reason not to try while mathematically possible," he added.
"If on a certain moment of the season we have no chances to get top four and we are still in the Europa League then nobody can criticise."
United will be without captain Wayne Rooney against Anderlecht while goalkeeper David De Gea faces a late fitness test.
Additional reporting by Reuters.