Diego Milito gave the hosts an early lead in the first leg before Salomon Kalou equalised for the Premier League leaders and Esteban Cambiasso blasted a 55th-minute winner for Inter.
NEWS: Inter edge Chelsea in last 16 opener
Kalou went down five metres out under Walter Samuel's challenge just before half time at a rocking San Siro but his appeals were waved away.
"I think it was a penalty in the first half but it's a penalty when the referee whistles," Ancelotti told a news conference.
"We wanted to play a game like we did. We did well, we leave with a result which is not positive but not dreadful.
"In the second game we will attack and try to score goals from the beginning until the end," added the Italian after his return to the famous stadium where he spent eight years as AC Milan coach.
Chelsea dominated for much of the first half with Didier Drogba crashing a free-kick against the bar among other chances.
"I think we can say we were unlucky this evening and we hope it will be better in the future. We played a good game, with personality and courage. We have to do the same in the next game with Inter," said Ancelotti of the second leg on March 16.
Inter coach Jose Mourinho, facing the side he led to two Premier League titles, was pleased with the result given the Italian champions went out to English teams Liverpool and Manchester United at the same stage in the last two seasons.
"I have to control my emotions. I have to be professional like I was today and like the Chelsea players were. When I go to Stamford Bridge I expect people to be pleased to see me back because we were so happy together," the Portuguese said.
"The most important thing is the result, we are ahead. We think we can win. Last year at Manchester United we lost 2-0 but we had great chances to score. We hit the post three times. Obviously we can score away."
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