And Papé, who started every game for France during the Six Nations, warned his teammates that they would have to bounce back quickly if they were to make the top six and the play-offs.
He said: "I'm frustrated by the defeat. There is disappointment because we wanted to get into the top five by beating Toulouse. That's not what happened, we lost. They played the perfect game away from home.
"They slowed down our game. They were right on the edge each time, but they did it well.
"There is a lot of disappointment, but we won't give up on anything.
"The season isn't over, we have four games left and we have to believe. Our aim was to remain unbeaten at home until the end of the season. For the sake of four points it's a shame."
Papé's frustration boiled over with ten minutes remaining in the game as he and Yannick Jauzion were sent to the sin bin.
But, with an Amlin Challenge Cup quarter-final with Exeter coming up on Saturday, Papé insists that Stade will need to release that frustration against the Chiefs.
He added: "We need to learn from this defeat. We are very frustrated and annoyed. We need to use that for next week and the week after.
"We aren't far away. We have the team we need."