Moise Kean fired Fiorentina to an early lead through a penalty, but Udines fought back to win via goals from Lorenzo Lucca and Florian Thauvin.
Runjaic beamed afterwards: "It was a very important victory, in a very difficult match: they were three very important points. I think that few people at the end of the first half would have thought of a comeback from us.
"We gave ourselves a great gift today: for us, for the club and for the fans. I am very happy. Now we have to look to the next match and close 2024 at home in the best possible way. We will try to win and improve the year overall.
"Some things can't be explained: I think that in the first half we played below par compared to what we expected. From my point of view, for me it's the same whether we play at home or away... we have to focus on ourselves and our level of performance".
On what he asked of the team at halftime, Runjaic also said: "These are things that stay in the locker room... they were emotional minutes but in the end the team did what I asked."
And on Thauvin, he added: "He works hard and as captain he has great responsibilities. He started off great but is now getting better and better. He is a great player and a great man, who understands football well.
"(Alexis) Sanchez? He is fine but he lacks game rhythm. We need to manage the ball better."