The Nigerian praised the recent performances of fellow midfielders Eden Hazard, Oscar and Willian as the club looks to keep pace with its title rivals after a slow start.
After a stuttering start to the season, the London side has won four of its last five Premier League games to leave them third in the table, just two points off table-toppers Arsenal.
Mikel highlighted the performances of Eden Hazard, Oscar and Willian, saying the attacking midfield trio are starting to acclimatize to high-stakes pressures at Stamford Bridge.
"[Mourinho] always wants us to play in a certain way and give 110 percent," Mikel is quoted as saying by The Sun. "If you don't, you're out. You don't want to slack, you don't want to sit down and think, 'You're the best, I don't want to defend or I don't want to run'. If you don't do those things, you don't play.
"That's the mentality he wants installed in this team and slowly but surely the likes of Eden, Oscar and Willian are beginning to do that."
Mikel said the club is seeking trophies, not just solid finishes.
"What the Premier League and Champions League means to this club. If you don't play for Chelsea, you don't know what these trophies mean to us," he said. "It's not a team where if you come second, third or fourth, it doesn't matter. No - every year you have to win something and this is the pressure.
"Now they're here, they have to feel the pressure and they are feeling it right now. That's why we just want to keep doing well and now they're starting to understand that we don't want to get beaten."