A calf injury sustained in the round of 16 defeat of Portugal - in which Cavani scored both Uruguay goals - kept the Paris Saint-Germain forward on the sidelines for Friday's clash.
And Cavani said it was the right decision by Tabarez not to include him in the matchday squad as he was not fit enough to be considered for selection.
"It was a very special week with a lot of expectation and I tried everything to be ready," Cavani said.
"I tried to do my best, but I was not one hundred per cent.
"But we have to be realistic, I did not feel for enough to play the 90 minutes, so it is best that your team-mates, who are better, play."
With Cavani sidelined, Uruguay struggled to create chances and were unlocked by France's extra quality in the final third.
"When you play in high intensity, this can happen to anyone," Cavani added. "This time it was our turn, but we have to continue because everything goes on.
"Before going to the field, I told them that I am very proud of them. I have affection for my companions and admiration for what they played.
"I am very proud to be part of this group. Regardless of the outcome."