Inter beat Juventus 2-0 last weekend to enhance its title credentials but could not follow that up with another win in Sunday's (AEDT) stalemate at Dacia Arena.
Relegation-threatened Udinese entered the game winless in eight but restricted Inter to minimal chances, the best falling to Lautaro Martinez in the first half.
Conte's frustration boiled over late on, the Inter coach receiving his marching orders because of dissent, although the Nerazzurri at least gained a point on bitter rival Milan, which was beaten 3-0 by Atalanta ahead of the sides' Coppa Italia quarter-final on Wednesday (AEDT).
Bayern Munich is the only side to have scored more goals in Europe's top-five leagues than Inter Milan this season but the visitors could not get going against Udinese.
Martinez had a goal correctly ruled out for offside from Inter's first meaningful attack and was denied by a superb one-handed Juan Musso save 15 minutes later.
Udinese otherwise kept their opponents at bay in a low-tempo first half, with Arturo Vidal and Ashley Young failing to truly test Musso from weak attempts.
Inter continued to lack ideas as the match wore on and was almost dealt a sucker punch when first Roberto Pereyra and then Rodrigo de Paul fired just wide of the target.
Achraf Hakimi lashed across the face of goal and a bad day for Conte got worse when he was booked and then sent off for protesting a decision that went against his side as Inter fired a blank for the first time in 22 league games.