Watched by club president Erick Thohir, who flew in from his native Indonesia on a rare visit to watch his team, Inter were jeered off the field by their fans after another frustrating evening in Serie A.
"I didn't like the first half, to be honest," Inter coach Walter Mazzarri told Sky Sport Italia.
"Udinese are a strong side who pressed us all over the field and closed down all the spaces.
"In the second half we deserved to score at least two or three goals especially in the last half-hour. We dominated the match and simply didn't score."
Scuffet, who has performed impressively for Udinese since being drafted into the side in February following an injury to Zeljko Brkic, capped his display with a stunning close-range save to deny Estebian Cambiasso in the 87th minute.
The teenager also foiled Hernanes twice and intercepted a dangerous header across goal by Mauro Icardi.
Inter, beaten 2-1 at home by Atalanta on Sunday after hitting the woodwork four times, are fifth in the Serie A with 48 points from 30 games, still on course for the Europa League, although Parma are only one point behind in sixth.
"I'm pleased to play well in an important stadium but you have to do well in every game," Scuffet said.
"I asked for (Inter goalkeeper) Samir Handanovic's jersey, as I've always said he was the reference point for me as a goalkeeper."
- Sports & Recreation