"It was the trophy we wanted for the last two months. You can't always get what you want and sometimes you are going to get second best. It's not a bad second best," admitted the New Zealander afterwards.
"Somebody mentioned earlier that for 20-odd hours we can be Heineken Cup and Amlin Cup holders and that is a pretty special thing. A third European trophy in three years. If you said that to me at the start of the season I would have grabbed it with two hands."
Stand-in captain Jamie Heaslip was full of praise for his side on a night that also saw the province's 'A' team lift the British & Irish Cup for the first time.
"(It was) a huge effort from everyone," said Heaslip. "Not just the lads who started the game but the lads that came on and the 'A' team who won the B&I Cup as well. A massive squad effort.
"Our changing room is buzzing. The scoreline flattered us at times. Stade really put it to us. It just seemed like we were tackling forever, but we showed how clinical we were with the ball."
Schmidt brought in a number of young players including Jack McGrath, Rhys Ruddock and Andrew Conway for the Challenge Cup decider, and the Kiwi praised the input of the province's up-and-coming talents.
"It is one of the great things about the squad. We managed to get the B&I Cup win tonight as well. It speaks volumes of the depth of the squad, looking at the number of the guys weren't available tonight and didn't play."
That leaves next week's RaboDirect PRO12 final against Ulster, a competition Leinster have failed to win since 2008 - indeed, they have been runners-up for the past three years.
"We have one match to play, so no matter what happens tonight we have to do our best next Saturday against Ulster," added Schmidt.
"I am a reasonably simple person. I just want to win next Saturday now. It is something that has eluded us. We will be looking to try to double up if we can."