The Italian club were knocked out of the Europa League after losing to Young Boys a fortnight ago but they could now end the Merseysiders' participation in the competition.
Defeat for Brendan Rodgers' side would see them fail to make the last 32, but if they at least match Young Boys' result at home to Anzhi Makhachkala, who have already booked their place in the next round, they will progress.
"We are sorry to be out of Europe because I see it as a failure, it's like we have not passed an exam," said Guidolin, whose side missed the knockout stage for the first time in the club's four seasons in the Europa League and - in the competition's previous incarnation - the UEFA Cup group stages.
He added: "But in sport, and in life, this is the way it is. We now have to show lots of pride and dignity and leave with our heads held high, as we have done for the last year-and-a-half in the Europa League.
"Last year we went through and this year we haven't, it means things have been more complicated this year and the difficulties were undoubtedly greater.
"Udinese are one of those little clubs who, many times over, have managed to play in Europe.
"This year, we have a different aim, but this club has always been able to build teams to perform in the league to earn chances in the Champions League and the Europa League, and I hope it will happen again."
Udinese forward Antonio Di Natale, who scored in the 3-2 win at Anfield in October, is keen for a European return next season but admits time is running out for him.
"I would like to play another campaign in Europe, but I don't know if I will," said the 35-year-old,
"I'd be proud (to play and equal the Udinese record of most European games held by Valerio Bertotto) but tomorrow is a big game as Liverpool come here to go through and the coach will make his choices accordingly.
"We need to play a good game, but if the coach gives me a minute, it is a big achievement to reach 33 games.
"When you play at this level, all games are beautiful. I hope to play again in Europe - I still have one and a half years left and I hope to play here again."