Joe Schmidt calls for officials to look at cheap shot on Sexton and high tackle on Kearney
Rory Best admitted Ireland blew a "massive opportunity" for victory in France that could well end their hopes of a third consecutive RBS 6 Nations title.
Ireland succumbed 10-9 in Paris, buckling under intense second-half scrum pressure, despite leading for the majority of the clash until Maxime Medard's late try.
Dave Kearney could miss the rest of the tournament with a shoulder injury, while head coach Joe Schmidt confirmed Sean O'Brien picked up another hamstring problem, Mike McCarthy was concussed and Johnny Sexton "knocked around".
Ireland paid the price for wasting a host of chances in the first half, with France's replacement props Rabah Slimani and Eddy Ben Arous turning the scrummaging screw when it mattered most.
"It was definitely a massive opportunity for us that we'll be very disappointed we weren't able to take, to push on and win that game," said Ireland captain Best.
"We know we had chances. When we look back at it later in the week we'll be really disappointed.
"We'll look in the second half on how we allowed our boys to get isolated at times."
France had telegraphed their scrummaging intentions by leaving set-piece specialists Slimani and Ben Arous on the bench and starting instead with inexperienced duo Jefferson Poirot and Uini Atonio.
Without the injured Marty Moore and the still ring-rusty pair of Cian Healy and Mike Ross, Ireland's scrum proved distinctly underpowered come Slimani's and Ben Arous' early second-half arrival.
Ireland sneaked through last weekend's 16-16 draw with Wales despite a severely creaking scrum, but this time their set-piece folded.
Medard scooted over after four consecutive five-metre scrums where Ireland were fortunate not to concede a penalty try or receive a yellow card.
Ireland boss Schmidt lamented his side's inability to build on the 9-3 half-time lead that came courtesy of Sexton's three penalties, before assessing the injury catalogue.
Ireland take on England at Twickenham on February 27, with Schmidt already accepting his resources could be further depleted.
"We're hugely disappointed with the defeat, especially having led 9-3 for so long," said Schmidt.
"Dave Kearney has suffered an AC (acromioclavicular) joint injury to his shoulder and that will keep him out for some time.
"Jared Payne played on with a dead leg for about 30 minutes.
"Johnny Sexton knows what he's going to get when he comes here, but he was pretty knocked around at the end of the game.
"Mike McCarthy certainly appeared to suffer a concussion, so he will now have to follow the protocols.
"Sean O'Brien suffered a hamstring injury. We feared it may have been his knee, the way he planted and turned."
Yoann Maestri's shoulder charge on Sexton and Guilhem Guirado's late, high tackle on Kearney could yet trouble the citing commissioners into action.
Ireland boss Schmidt hinted he would want the Six Nations disciplinary bosses to review both incidents.
"Those aren't for me to say, they are for the referee to look back at," said Schmidt of the two first-half incidents.
"I would encourage the referee organisers to look back at those.
"We were given very clear guidelines of what would be tolerated and what wouldn't.
"But that's entirely outside my gambit."
France boss Guy Noves insisted there was more to Les Bleus' victory than simply the ruse of delaying Slimani's and Ben Arous' entrance until the second half.
The France boss admitted his pack "made the match tilt" with the sequence of five-metre scrums and penalties before Medard's try, but refused to base the entire victory on that plan.
"I don't want to hear that changing the props was the right strategy," said Noves.
"The whole staff has been working hard.
"When you win they say it's good strategy, when you lose they say it's not.
"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 victory depends on the choices made by the players and especially the captain, who decided to take that touch at 9-3 instead of kick at goal.
"They took the touch, there was that scrum, and the beautiful try they scored.
"The players won, not the coaching.
"The scrum was pivotal for the victory. The referee had trouble with the decision. We expected a yellow card.
"But the French forwards made the match tilt at that moment, allowing the backs to score that try."