Games went with serve until the fifth game of the second set when Sitak was broken and the 12th seeds were able to go on and close out the set to force a decider.
There was nothing between the teams in the final set and Sitak felt they had a good chance to cause an upset.
"It was just a few points, second set and third set, we got broken at 2-2 in the second set but I think we got our groove back on in the third set and we were on top of them. We had looks on their serve but couldn't convert. Then at 4-all with Nick serving it was a long game and they came up with the goods. Sometimes it doesn't go your way."
The result has continued a disappointing run through the clay court swing for the pair who will now turn their attention to the grass court season in the run in to Wimbledon.
But Sitak's campaign in Paris is not yet over. He is in the mixed doubles draw with Ukraine's Elina Svitolina and is likely to start his campaign on Friday.
Marcus Daniell has followed Artem Sitak out of the doubles with a 6-4, 6-4 defeat by the 7th seeds, Spaniard Marcel Granollers and Croatian Ivan Dodig.
Matt Brown is in Paris thanks to Emirates Airline