Despite taking the first set 6-1, world number two Nadal lost the following sets to his Croatian opponent 7-6 7-6.
However despite exiting the Montreal-based competition at an early stage, the 25-year-old believes that he couldn't have done much more to win the match.
"I seriously didn't feel that I played that badly today," said Nadal.
"Possibly I could have performed better on the bigger points but overall I played well enough to win.
"That's just tennis though. The only thing I can do is congratulate my opponent."
Dodig will now face Serbian Janko Tipsarevic in the third round this evening.