Yannick Jauzion, Patricio Albacete and Cedric Heymans crossed for the French giants in an accomplished performance to set up a mouth watering semi-final with Leinster.
But Toulouse scrum-half Kelleher has demanded more from his team-mates ahead of the May 1 clash.
Kelleher, 34, said: “I watched Leinster play on Friday night and they are as good as anyone else.
“Seeing the level of rugby this weekend means our performance will not be sufficient to win the next game. Leinster are a difficult team but we will enjoy the win tonight, celebrate and worry about them in the coming weeks.”
Stade Francais briefly threatened a shock when skipper Rodrigo Roncero scored the first try. But France centre Jauzion tipped the balance with a try on the stroke of half-time to nudge Guy Noves’ men 13-10 ahead.
The hosts cut loose in the second half with David Skrela notching up an impressive 27-point tally.
Kelleher believes Toulouse will be in the right frame of mind for the semi-final.
He added: “The knockout stages are all about taking your chances because they don’t come around too often. You may only get one or two opportunities.
“Quarter-finals and semi-finals are when your playmakers come into their own and players who can make the right decision become highly important.”
Stade omitted England flanker James Haskell from their 23-man squad but coach Jacques Delmas rejected talk that the player was dropped following a club v country row last month.
Delmas said: “We didn’t pick James because we wanted a different line-out option. The reason he wasn’t on the bench was because we wanted a specialist number eight on the bench in case of injuries.”
Toulouse scorers: Tries: Jauzion, Albacete, Heymans. Cons: Skrela 3. Pens: Skrela 7.
Stade Francais scorers: Tries: Roncero. Cons: Beauxis. Pens: Beauxis 3.
TOULOUSE: C Poitrenaud (M Medard 66), V Clerc, F Fritz, Y Jauzion, C Heymans, D Skrela, B Kelleher (N Bezy 73), J Poux (D Human 50), W Servat (V Lacombe 69), B Lecouls (C Johnston 41), R Millo-Chluski (Y Maestri 41), P Albacete (G Lamboley 71), J Bouilhou, T Dusautoir [capt], L Picamoles (S Sowerby 50)
STADE FRANCAIS: H Southwell (G Messina 57), J Arias (I Mieres 72), M Bastareaud, M Gasnier, M Bergamasco, L Beauxis, N Oelschig; R Roncero (capt) (R Slimani 1), D Szarzewski (A Marchois 62), S Marconnet (R Gerber 73), T Palmer, P Pape, A Burban (B Kayser 60), P Rabadan (S Taylor 41), J Leguizamon
Sin Bin: Taylor (70).
Referee: A Lewis (Ireland).