Toulouse skipper Thierry Dusautoir was a frustrated man after Sunday's agonising loss to Leicester at Welford Road.
The 9-5 defeat saw the four-time champions crash out of the tournament as they left 17 points by the wayside from the kicking tee and were refused a try by the TMO, who was unable to see clear evidence of the ball being grounded.
"There are regrets because we played a better match than Leicester," said Dusautoir after the game.
"We were generally on top overall. We just didn't take our chances.
"In seven years, it's the second time that we're not in the quarter-finals. We're a big club and we'll take lessons from this elimination.
"The conditions were really bad with wind and snow. We had a go nevertheless and created opportunities and we scored a try.
"Our elimination was not just down to today, if we had always played like that we would have easily finished first.
"We lost a lot of balls at the line-outs that we could have used. We really need to be better there."
Iconic Toulouse coach Guy Novès was stoic in defeat.
"Destiny decided Stade Toulousain wouldn't go into the quarter-finals this year," said Novès.
"Everyone saw that we left nearly 25 points by the wayside. 17 points from the boot with penalties that were kickable. It's the first time that I saw us fail that badly in that sector.
"We almost have to laugh at ourselves.
"We saw a real Toulouse team that had the opportunity to score 30 points but due to lack of finishing ended up only scoring 5. "