The Friuli lost 6-5 on penalties to its Portuguese opponent to miss out on the competition proper and Guidolin said afterwards that he would 'go home, rest and consider my future'.
He then asked to meet with club owner
"Guidolin is and will still be Udinese's coach," Pozzo told Udinese Channel.
"His bitterness and the words he spoke yesterday came from the fact he is a very sensitive man, he always gives 200 per cent in what he does and always manages to transmit it to the squad.
"Those words come from the disappointment we all felt last night.
"Needless to say we totally believe in him: he is loved by the Friulian people and he feels this love. He loves Udine, its people, Udinese.
"He has a long contract with us and he feels happy to continue working for our club.
"I talked to him this morning and, even though I can understand his disappointment, I made him understand how much we believe in him and that, although we feel sorry for how it went against Sporting Braga, it's all over now.
"Now we turn a new page, all together."
AC Milan chief executive Adriano Galliani has denied falling out with club president Silvio Berlusconi, despite reports to the contrary.