Hosts France came from behind to beat 10-man Ireland 2-1 and reach the
A tactical switch from coach Didier Deschamps at the break revitalised the French, who struggled to find their feet early on after conceding a Robbie Brady penalty in the second minute, the fastest goal in the 2016 tournament.
France will play either England or Iceland at the Stade de France next Sunday.
"We have difficulties getting into games, we saw that again today, and that's something we have to work on," said Griezmann.
"Finding ourselves trailing made it difficult but we showed we've got heart. Things were said in the dressing room at halftime and in the second half, it was a different France team."
It was the worst possible start for the hosts when midfielder Paul Pogba clumsily barged over Ireland's Shane Long in the penalty area, allowing Brady to dispatch the resulting spot kick to go 1-0 up on the second minute.
Finding themselves behind for the first time in the tournament, the hosts seemed to lack the urgency to wrestle control of a stop-start first half.
Their best chances fell to Griezmann who headed over the bar from close range, while a late strike by Dimitri Payet whacked into the Irish defence who desperately guarded their goal.
At the other end, Ireland didn't really threaten apart from a bouncing shot from striker Daryl Murphy that forced keeper Hugo Lloris to dive to his left.
A flat first half ended with the French players trudging off to the noise of loud booing from the packed home support.
Deschamps switched things up after the break, bringing on flying winger Kingsley Coman for holding midfielder N'Golo Kante and moving playmaker Pogba into the middle and Griezmann into a more central role behind strike partner Olivier Giroud.
The strategy paid dividends immediately as France stretched a tiring Ireland. Griezmann equalised in the 58th minute from a Bacary Sagna cross, and then fired his team in front three minutes later when Giroud nodded the ball down into his path.
Another surging run from Griezmann saw him chopped down on the edge of the area by Shane Duffy, earning the defender a red card as the game started to look beyond the Irish.
All was forgiven by the French crowd, who broke into a deafening 'Marseillaise' and cheered their team all the way to their first knockout stage win in the competition since winning Euro 2000.
On a bum note, though, Kante and defender Adil Rami picked up yellow cards and will miss the quarter final through suspension.