The holding midfielder felt his side should have done better and stressed that they wanted to bag the full three points
Ricky Alvarez opened the scoring after 16 minutes, but the Nerazzurri were unable to hold on to their lead as German Denis restored parity for the Bergamo side before the break, much to the disappointment of Cambiasso.
"Atalanta were certainly happy to take a point off Inter. We wanted all three, we always go for three points no matter where we're playing," the Argentine midfielder told Inter Channel.
"We can't be too disappointed at drawing a match in Bergamo if we think of all the problems this fixture has caused us in recent years.
"However, we didn't want to settle for a point and we showed that until the end, trying everything to get the win. Unfortunately it didn't come off for us."
Inter currently sit fourth in the Serie A table with 19 points from 10 games, though Fiorentina could leapfrog them if they defeat Napoli on Wednesday.