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The Irish lost a 9-3 half-time lead as Sean O'Brien, Dave Kearney, Johnny Sexton and Mike McCarthy were all forced off as France snatched victory.
"France came out in that second half and played very strongly," said the Ireland coach after the game in Paris.
"On the back of that we were starting to lose our legs a little bit."
As the Six Nations holders tired, Maxime Medard's 70th-minute try helped seal France's narrow win with Jules Plisson's conversion seeing the hosts secure victory.
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O'Brien was forced off by a hamstring injury in the 19th minute while Schmidt said wing Kearney is likely to miss the remainder of the Six Nations after sustaining a shoulder injury before the interval.
Lock McCarthy (concussion) will be another doubt for the game against England on 27 February while fly-half Sexton had to be replaced with 10 minutes remaining after taking several heavy hits.
Schmidt also revealed that centre Jared Payne had been forced to soldier on in the closing 30 minutes despite suffering from a dead leg.
Keith Earls and Simon Zebo missed Saturday's defeat because of injury after starting in last weekend's draw against Wales while Schmidt was also without the likes of Peter O'Mahony, Iain Henderson, Tommy Bowe, Mike Ross and Cian Healy in Paris.
The Irish coach said he was not surprised that former Racing Metro fly-half Sexton had been on the receiving end of some French physicality.
"He knows what he's going to get when he comes here," said the Ireland boss."He was pretty knocked around by the end of the match."
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Schmidt expects the match's citing commissioner to examine a number of incidents in the match - including Yoann Maestri's first-half late hit on Sexton.
"We had some very clear indications coming into the Six Nations about what would be tolerated and what would not be and what sanctions would follow," the New Zealander said.
"There's a fair degree of frustration, but some of that reflects the frustration at ourselves for not taking the opportunity - to lead 9-3 for so long when we had a couple of opportunities in the first half in tough conditions to maintain possession.
"It was a very greasy surface but at the same time you have to play those conditions.
"We were unable to capitalise on what was a pretty strong kicking game early on."
The 45th-minute introduction of props Rabah Slimani and Eddy Ben Arous helped turn the contest in France's favour but home coach Guy Noves insisted that there was more to his side's victory.
"I don't want to hear that changing the props was the right strategy," said Noves.
"What we were doing from the 30th minute to the end, that feels good, that was the right way.
"The players really focused hard to rectify the mistakes from last week. The players won, not the coaching."
Ireland coach Joe Schmidt was left "hugely disappointed" after his injury-ravaged side were beaten 10-9 by France in a bruising Six Nations contest.