The German's departure was confirmed by the club on Monday, bringing an end to a spell of more than two years in charge. Runjaic paid the price for a difficult opening to the Serie A campaign, with Udinese collecting just five points from their first 10 matches through one victory, two draws and seven defeats.
The decisive setback was their 5-2 home defeat against Roma, which left the Friuli club second from bottom in the table.
In an official statement, Udinese thanked Runjaic and his assistants Przemyslaw Małecki and Alexander Trukan for their work.
"The club and the coach part ways after more than two years marked by the achievement of important objectives," the statement read. "The club sincerely thanks Kosta and his staff members Małecki and Trukan and wishes them the very best in their future professional endeavours."
There was also a personal message from former Udinese captain Thauvin, who is now playing for Lens after leaving the Italian club.
The French forward took to social media to acknowledge the influence Runjaic had on his career, particularly the confidence the coach showed in him during their time together.
"Personally, I wanted to thank you for the moments spent at Udinese. It was an honour for me to work with you and your staff. You are great professionals and I learned a lot from you," Thauvin wrote.
"You believed in me when very few people still did. You gave me confidence and the opportunity to demonstrate my value on the pitch. You were the first coach to appoint me captain. Thank you."
Thauvin also extended his message to Małecki and Trukan, wishing all three well with their future challenges.
Udinese have moved quickly to appoint Runjaic's replacement, confirming Zanetti as their new head coach on a contract running until 30 June 2027.
The 43-year-old returns to Serie A after previous spells with Venezia, Empoli and Verona. His coaching career began with Südtirol before he moved to Ascoli, while his breakthrough came in 2020-21 when he guided Venezia to promotion to the top flight after a 19-year absence.
He subsequently managed Venezia in Serie A before taking charge of Empoli, where he secured a comfortable mid-table finish in 2022-23. His most recent top-flight appointment was at Verona, whom he led to 14th place in 2024-25 before leaving in February 2026.
Zanetti will take his first training session with Udinese on Tuesday, with his official presentation scheduled for Wednesday.
His immediate task will be to arrest the club's slide and lift a side that has struggled badly during the opening weeks of the campaign. After Runjaic's dismissal, Udinese are hoping a change of leadership can provide the response required to move away from the relegation places.