His side were beaten 3-0 away from home by title rivals Rijeka on Sunday.
The result sees Rijeka leapfrog their opponents into first place with just 10 matches remaining.
Hajduk now sit two points adrift heading into the international break as they bid to win a first league title for 20 years.
Gattuso was still furious as he appeared live on Croatian TV for a post-match interview.
During the heated segment, the World Cup winner clashed with pundit Josko Jelicic, who won the title with Hajduk as a player.
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The pair argued in English, Spanish and Italian as presenter Valentina Miletic struggled to calm the pair down.
As he arrived at the pitchside desk, Gattuso snubbed a handshake with Jelicic, exclaiming: "I don't shake hands with you as you speak too much."
He then added: "You speak too much and you don't have respect for the people. You played football so you know very well the situation.
"You always speak very bad. I don't have respect for you. You speak very bad."
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Jelicic hit back, though, replying: "You played very badly," prompting an irate Gattuso to raise his finger to him.
The Italian responded: "You have to have respect for people. I am speaking."
His antics angered the former Hajduk midfielder, who snapped: "Put your hand down. You have to respect me."
Tempers continued to rise between the pair, with Gattuso telling Jelicic: "Speak here. Speak of football here."
The pundit replied: "We are going to speak. I am here," prompting the Hajduk boss to shout: "Speak! Speak face to face."
Gattuso continued his rant, exclaiming: "You are speaking to someone who has won everything in the world.
"I don't want to speak with him. This is the last time, if you are here, I won't speak to the TV because you are a bad person."
Jelicic then told him: "You are a foreigner, you need to respect everyone here."
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However, Gattuso continued to refuse to speak to the pundit as he finally began the interview, finishing by stating: "I won't speak with you, ok? Let's go."
The former AC Milan and Marseille boss has been in charge of the Croatian side since the summer.
He has won 16 of his 33 matches across all competitions after penning a deal through to 2026.
His side are chasing the sixth league title in their history and a first since 2005, but now sit two points adrift of Rijeka.
The two sides are scheduled to meet for the final time on the penultimate matchday of the season.
Hajduk will host their title rivals at Stadion Poljud in Split on May 17.
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Despite winning the World Cup, two Champions Leagues and a pair of Serie A titles as a player, Gattuso has only lifted silverware once as a coach.
His only managerial honour to date came with Napoli in 2020 as they won the Coppa Italia under the 47-year-old's guidance.