Cattermole is in line to return to the Black Cats' line-up at Aston Villa on Saturday after completing a three-game suspension following his red card at Hull.
And despite disciplinary problems which have seen Cattermole sent off eight times in his career, Poyet reiterated the 25-year-old's importance to his long-term plans.
Poyet said: "I need to make sure Lee knows he is important to the team, and Lee needs to make sure he keeps his cool a little bit better.
"He's an important player - he's a leader, he's strong and he doesn't accept defeat - and sometimes you need those kinds of characters."
Poyet will also be boosted by Wes Brown's availability for the trip to Villa after his own controversial sending-off at Stoke last weekend was rescinded by the Football Association.
Poyet added: "I think it is important for many reasons because we are trying to create some consistency in the team especially at the back, because I think we are getting better.
"When you have a player like Wes in your team it's definitely a little bit easier. We had a couple of interesting days waiting to see if he would be available, and after his clearance it made our preparations a lot easier."
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