Chelsea, whose defeat was compounded by the loss of goalkeeper Petr Cech with a calf injury in the second half, were a goal down inside three minutes when striker Diego Milito put Mourinho's side ahead.
Related ArticlesInter Milan 2 Chelsea 1Kalou: referee got penalty call wrongMourinho: I am lucky at Stamford BridgeChelsea blow as Petr Cech suffers calf injuryInter Milan v Chelsea: as it happenedChampions League actionSalomon Kalou equalised in the 51st minute but Inter restored their advantage four minutes later when Esteban Cambiasso drilled in the winner.
Kalou's goal may yet prove to be the pivotal moment of the tie when the two teams meet again in the return leg next month.
"I think that what we saw tonight, we have the chance to turn it around," said Ancelotti.
"I think we played well. We leave without a positive result, but it's not an ugly one either.
"We will play to attack and win the second leg in the same way we did in this game.
"We tried to attack and score from the first to the last minute."
Meanwhile, Cech will undergo further assessment on his injury today after leaving the field on a stretcher.
The Czech Republic international collected a cross, rolled the ball out and then immediately signalled to the bench that he could not continue.
But initial fears that he had damaged knee ligaments were quashed by Ancelotti after the game.
"We have to wait and control his condition over the next few days," said Ancelotti.
"He has an injury on his calf. We cannot say now when he will return to the squad."
Chelsea felt they should have had a penalty in first-half stoppage time when Kalou was brought down by Walter Saumel, but referee Manuel Mejuto Gonzalez waved appeals away.
However, Ancelotti refused to pin the blame on the ref. He said: "I know Mejuto Gonzalez is a very good referee with a lot of experience and I don't want to say anything else.
"We can say that we were unlucky this evening and we hope that will be better in the future.
"I think there was a penalty in the first half, but a penalty is only when the referee whistles."