United face Anderlecht on Thursday night in the first leg of their Europa League quarter-final tie before hosting the league leaders this weekend.
Mourinho’s men currently sit fifth in the league, four points behind fourth-placed Manchester City, and now face a fight to secure Champions League football after a one-season absence from the competition.
"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. The football country would kill me," Mourinho said.
"There is no reason not to try while it's mathematically possible. 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.”
Mourinho is also hoping to head into Sunday’s clash with a clean bill of health.
"I hope we have no more injuries, no more suspensions and I hope the players keep showing amazing character to keep going and going. Until it's not possible we are going to fight for the top four," he added.
United will be without captain Wayne Rooney against Anderlecht on Thursday while goalkeeper David de Gea faces a late fitness test.