The midfielder only completed his move from Tottenham to Inter on Tuesday, but came off the bench as the Nerazzurri booked their place in the Coppa Italia semi-finals with a 2-1 win.
Speaking after the game, Conte revealed a lack of midfield options was the reason Eriksen came on with 24 minutes to go, but was pleased with what he saw.
"We did not intend to use Eriksen so soon, as he only started training with us yesterday, but Matias Vecino and Barella were the only available midfielders," Conte told Rai Sport.
"Eriksen has character and raises the quality level of the squad. I hope to get more players back, because we really are limited in the middle."
Eriksen thought he had capped his debut with an assist, only for Lautaro Martinez's goal from his through ball to be ruled out for offside.
However, it was still an assured cameo appearance from the Dane and Inter fans can look forward to seeing plenty more from him.
Earlier, Martin Caceres had cancelled out Antonio Candreva's opener prior to Nicola Barella's wonderful half-volley, which sealed the win, 42 seconds after Eriksen came on.
"I tried and it went right into the far bottom corner. I must learn to score easier goals," Barella joked after the game.
"We deserved this victory. We must give more in Serie A, but we've also been a little unlucky in some circumstances. There's time, it's a long campaign."