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Stefano Pioli explained that his Milan side avoided discussing Inter's earlier win ahead of facing Genoa.
Milan claimed a 2-0 victory thanks to goals from Rafael Leao and Junior Messias in San Siro on Friday.
Their game came hot on the heels of Inter's 3-1 victory at Spezia, a result that had seen the reigning champions briefly move into top spot in Serie A.
However, Milan got the job done, winning for the first time in three games to restore their two-point advantage with five matches left, though Inter do have a game in hand.
Milan are attempting to win their first Serie A title since 2010-11 and Pioli noted that although he knew Inter had won, his side had not discussed the possible ramifications.
"I knew their result, but we didn't talk about it with the team," he told DAZN.
"We had to go back to winning. We knew that whatever happened, we would try to win every game.
"I think we had the right approach and hunger this evening, we ran very few risks and that is an important factor."
Pioli suggested it is difficult to know how to best handle the pressure of the title race, though he backs the character of his players.
He added: "We have to keep going, the tension is rising and so is the pressure. Now we have to feel the pressure as nothing but positive energy.
"Every day [in training] I am undecided whether to increase the pressure or to release it. But, I have to expect a lot from these guys because they are strong.
"We are more aware of our strength, I am pushing for this. There are few games left and we have to do well. Many of us are fighting for the Scudetto for the first time, it is a path that will help us. We want to be winning again."
Milan kept a sixth straight clean sheet, making Pioli only the third coach in the club's history to achieve such a feat in a single Serie A season, after Fabio Capello (twice in 1993-94: seven and nine) and Nereo Rocco (seven in 1971-72).
Key to that has been the form of goalkeeper Mike Maignan, who made a stunning save to deny Genoa's Hernani a consolation in stoppage time.
"We have to continue like this," Pioli said. "Maignan is incredible, he is receiving the right compliments. He must give his contribution to this young team."
Milan have picked up more than 70 points after 33 Serie A games for the first time since their last Scudetto-winning season 11 years ago.