Ranieri's captain Francesco Totti was sent-off on the night, while there were scuffles between the players during the 90 minutes.
"We took a long time to get going, evidently this meant a lot to us and the pressure got to the team," said Ranieri.
"We were penalised by an incident just before half-time, we gave our best, so our compliments go to Inter.
"We wanted to play ball to feet, as we know that if we play long then we cannot fight Inter.
"We struggled more than expected to play our football and then conceded when we lost the ball in midfield, which is their favourite tactic."
He added: "We honour the victors. Inter came here, played a good game and won, so we compliment them."