The Argentine felt the Nerazzurri gave 100% but just didn't have enough to halt the charge of the Serie A leaders
Rudi Garcia's supreme start to life with the Giallorossi went on at San Siro as his side secured a seventh Serie A win from as many games this season, with Francesco Totti scoring twice and Alessandro Florenzi netting in the second half.
Totti's second came from the penalty spot, although Alvaro Pereira's foul on Gervinho appeared to be outside the box, but Cambiasso refused to make any excuses for his side, admitting Roma had simply been better.
"Credit to Roma," the 33-year-old said. "We wanted to take the game to them and we had a spell of good football, possession and chances too.
"But it's goals that matter in this game - when you concede and when you score - and if they get more than you then that's how it ends up.
"The foul that led to their penalty was outside the box but we're not looking for excuses.
"Sure, it came at the worst time possible, just as we were hitting back after their opener, and we'd had two chances just before then. I think the post is still shaking from (Fredy) Guarin's shot.
"We did everything we could do and the fans saw that too. We have to keep going and we'd have said the same thing if we'd won. There's a long way to go and we must concentrate on getting back on track.
"We played more football but couldn't pull it off. It's just one of those nights, there's no point looking for excuses. Hats off to them, they played well.
"We're disappointed because you never like to lose, but the league is a marathon. We'll try to make up the dropped points and climb as high as possible."
Inter will resume their league campaign after the international break with a trip to face Torino.