The result leapfrogs the Friulani into fifth place - just three points shy of the Viola in fourth - and Milan's slip with Atalanta means it's all to play for.
"It was a great game between two teams who tried to go for the win," said Prandelli. "We deserved to get back into it with Christian Vieri's goal, but then were caught out. A team like ours cannot concede a goal like that on the counter-attack and affect our whole match.
"This is a missed opportunity, because the team played well and should have shown more character. It's true Adrian Mutu and Fabio Liverani were suspended, but that doesn't excuse who played today."
Christian Vieri managed to level Gokhan Inler's opener for Udinese before efforts from Antonio Di Natale and Fabio Quagliarella settled the match.
"It was an entertaining encounter and both sides enjoyed their football," said Udinese coach Pasquale Marino.
"We were helped by the fact we broke the deadlock early on, but I think overall it was a deserved victory. We had a period of difficulty and now we're visibly improving in terms of performance, fitness and confidence.
"Will we aim for fourth place? We have not talked about it and will only focus on the next game at Siena."