Atalanta have won only one of their past five matches in all competitions - losing the other four.
Their latest disappointment left them sixth in Serie A, five points behind fourth-placed Milan.
Atalanta face league leaders Napoli next weekend and will almost certainly be without midfielder Teun Koopmeiners after he went off shortly before halftime with what looked like a hamstring injury.
The home side improved after the break and pressured Udinese but with 67 per cent possession and 14 shots on goal overall, were unable to find the net.
Udinese goalkeeper Marco Silvestri was made to pull off a stunning stop in the final minute to deny Rafael Toloi.
Atalanta are currently in the Conference League spot but will be hoping for more.
AAP