The Blues manager wants his side to rise to the challenge of a Premier League title push as it prepares to face three teams scrapping at the bottom of the table.
The Blues sit second in the table, four points behind leader Arsenal, and beat Southampton 3-1 on Sunday to record back-to-back league wins going into three fixtures against teams battling at the wrong end of the table.
Away trips to Sunderland and Stoke City will be followed by Crystal Palace at home but Mourinho has no plans to set "targets" for his side, demanding only that it rises to the challenge of chasing down the Gunners.
"If you are 10 or 12 points behind, you are building but you are not fighting for the title," the Portuguese manager told the press. "If you are three, four or five behind, you are building evolution but fighting for the title. One of the things these boys have to learn is to cope with the responsibility of being there. We cannot be 15 points behind by December; we have to be there.
"Now we have two matches away and, after that, we play Crystal Palace at home. We are playing against three teams which need points because of the positions they have and we are going to have three very difficult matches. I think my team is a team that prefers that I [don't] establish targets. I can't say now I want to win five consecutive matches, now I want to be top of the league. ... I want nothing. I just want to work with them and feed the young players."