Milan's lead was cut to two points at the weekend as they crashed to a 1-0 defeat at Palermo while both Inter Milan and Napoli won.
The top three are now separated by just three points ahead of the Milan derby on April 2, which if won by Inter would see the champions go top for the first time this season.
They have closed the gap to Milan from 13 points (with a game in hand) in mid December and Gattuso admits the leaders are feeling the pressure.
They have picked up just one point from their last two games against rock-bottom Bari and a Palermo side that had suffered five straight defeats before playing Milan.
"There's always fear because having earned just one point from our last two games makes you realise that there are worries," he told Sky Sport 24.
"We conceded two naive goals in the last two games, we created many chances but scored just one goal.
"We need to be more ruthless, more clinical and we also need a bit of luck.
"We know that right now we need to do something more, what we're doing isn't enough."
But Gattuso insists it's not as clear a cut case as Inter storming back at a faltering Milan and claims Inter aren't the favourites for the derby.
"Inter also struggled to beat Lecce at home (1-0), there aren't any easy games," he added.
"The more you go forward, the more the games are difficult. We have a lot of respect for Inter and we have to prepare well for the derby.
"Wins give you conviction and right now Inter have more of that than us. They've been winning for the last four or five years and that gives you strength.
"In the years when we were winning often, in the difficult moments we always managed to pull it out of the bag because victories give you greater knowledge and strength."
Although Gattuso has been with Milan since 1999, the 33-year-old admitted he is considering an approach for next season from Russians Anzhi Makhachkala, for whom former Brazil and Real Madrid full-back Roberto Carlos already plays.
"There's been an approach but we're a long way apart," said Gattuso of the interest from the Dagestani team.
"I have a family, I don't take decisions on my own but Milan is my home, you don't forget 12 years.
"Right now the objective is to win this championship and that's all I'm thinking about.
"You never know in life but Milan is my home."
Gattuso fears Milan will blow title
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