Following his arrival from Tottenham, Eriksen came off the bench in the midweek Coppa Italia tie against Fiorentina, replacing Alexis Sanchez.
The Denmark international was handed the chance to start for the first time in Serie A on Sunday, recording 51 touches and completing 78 per cent of his attempted passes before he was replaced in the 58th minute.
It was 0-0 at the time of the change but Inter went on to collect all three points thanks to a Romelu Lukaku brace, taking the Belgian's tally in Serie A this season to 16 goals.
Conte – who saw his team end a run of three successive league draws – called for patience with Eriksen, despite expressing his satisfaction with the 27-year-old's efforts during his time on the pitch.
"I think that for someone who arrived five days ago, and we should not forget we had to rush him in because we were missing several midfielders, Eriksen still made a positive impact," Conte told Sky Sport Italia.
"Obviously, he needs to get settled into our style of football and also find the right fitness levels for Serie A, but I am very pleased with his full debut.
"He will get to learn the positioning we ask of our midfielders, but these are early days and I am satisfied."
After opening the scoring with a left-footed shot in the 64th minute, Lukaku converted from the penalty spot following a foul on substitute Sanchez.
The result sees Inter move above Lazio into second place in the table, three points behind leaders Juventus, ahead of next weekend's Milan derby at San Siro.
"The match against Fiorentina in the Coppa Italia gave us a boost," Lukaku told Sky Sport Italia. "We knew that it wouldn't be easy here in Udinese, but in the second half we did well.
"We managed to score two goals and get all three points. It's an important victory on our journey. We must now keep this up and turn our attention immediately to the derby against Milan."