La Rochelle beat Gloucester to reach Champions Cup last-eight
Gloucester led by four points with just three minutes left on Saturday before Thomas rescued the defending champions from France.
La Rochelle will face either three-time champions Saracens or the Ospreys, who meet on Sunday.
"It's good that we won, but what we did is not satisfactory or worthy for champions," Thomas told France Televisions after his side conceded three tries.
"It showed we have character though, even when things are difficult we managed to react."
The sides were level 15-all at the break as hooker Pierre Bourgarit and Thomas went over for the hosts and centre Chris Harris and lock Freddie Clarke did so for the English outfit on the Atlantic coast.
Ex-All Blacks scrum-half Tawera Kerr-Barlow sniped over from short range with 35 minutes to play before Gloucester then led 26-22 after two Billy Twelvetrees penalties and a try from Wales winger Louis Rees-Zammit.
The champions faced a tough task to keep the defence of the trophy alive but 29-year-old Thomas claimed his second try of the game with three minutes remaining to the joy of a sell-out crowd at Stade Marcel-Deflandre.
Elsewhere, five-time winners Leinster will host English champions Leicester after they claimed the Irish derby spoils by 30-15 over Ulster at Lansdowne Road.
More than 50,000 people braved the torrential rain in Dublin two weeks after Ireland claimed a Six Nations Grand Slam, but the hosts were without injured fly-half Johnny Sexton.
Sexton's replacement in the provincial No. 10 shirt Ross Byrne kicked 15 points as scrum-half Jamison Gibson-Park, lock Ryan Baird and prop Andrew Porter scored tries.
