Walter Mazzarri's side were beaten in a home Serie A match for just the second time this season on Sunday, losing 2-1 to in-form Atalanta.
Defeat was a bitter pill to swallow for Inter, who dominated the second half and hit the woodwork twice before Giacomo Bonaventura netted a 90th-minute winner for the visitors.
The mood at Inter is very different this season, though, and the home players were clapped off San Siro despite the defeat.
The club recorded a disastrous ninth-placed finish under Andrea Stramaccioni last term that saw them miss out on European football, but a takeover from Indonesian businessman Erick Thohir, together with Mazzarri's brand of football, has revived hopes among Inter supporters.
They sit sixth in the table – just four points behind fourth-placed Fiorentina – and defender Jonathan was upbeat despite defeat on Sunday.
"There was disappointment in the dressing room, but we were also relaxed because our fans applauded us after the final whistle," he said.
"We know losing is part of football. In the next game, against Udinese, we hope to start out focused from the opening whistle."
Inter midfielder Hernanes added: "Physically we're in good shape and ready for a fantastic end of the season.
"I'm pleased we have another game so soon (against Udinese) and we want to do our best."
Colombian Fredy Guarin signed a new contract on Monday, a further show of faith in Thohir's attempts to reverse Inter's fortunes.
Mazzarri's men were six matches unbeaten before Sunday's loss to Atalanta and their defence has been rock-solid, giving up just four goals in their last seven outings.
Juan Jesus is available again after a three-match suspension for Inter, who are likely to recall Yuto Nagatomo to their starting line-up.
Udinese arrive in Milan off the back of a 1-0 win over Sassuolo on Sunday, a result that extended their unbeaten run at home to four league matches.
Yet Francesco Guidolin's men have displayed poor form on the road, winning just three out of 15 Serie A away games so far this term.
Veteran striker Antonio Di Natale notched his 10th Serie A goal of the season on Sunday and continues to be the club's most reliable threat, but Udinese – who will be without suspended defender Dusan Basta - need more from fellow forward Luis Muriel.
The two sides have already met twice this season, with Inter winning November's reverse league meeting 3-0.
Udinese hit back with a 1-0 defeat in the last 16 of the Coppa Italia, a competition they reached the semi-finals of before losing to Fiorentina.
