It took a late try from Samoan international centre Paul Williams to put the French side through to their second successive semi-final and the possibility of salvaging something from their lacklustre season.
Cheika said: "I think that we wanted it more in the end because they had plenty of ball. We knew that they were a good team because we had scouted them a lot so we knew exactly what we were in for.
"We said at half-time that this one was going down to the wire and it certainly did. For use backing up from the match against Toulouse [in the French top 14], which was a huge disappointment for us, was really a great effort by the team.
"I reckon that Exeter are going to make the [Premiership] top four because I think that they believe in themselves. They look like they are very well coached, he's got them very well drilled."
Exeter went in to the break 9-6 ahead as Argentinian international fly-half Ignacio Mieres landed three of his four penalty attempts with Stade Francais replying with two from their scrum-half Julien Dupuy.
The home side went in to the lead for the first time early in the second half with a try from full-back Djibril Camara before Dupuy added penalties either side of one from Mieres.
Chiefs' replacement Sireli Naqelevuki went over for the visitors first try to level the scores. The game looked to be heading for extra time until Williams strolled over the line to seal the game.
While Stade Francais have booked a second successive Amlin Challenge Cup semi-final place, Exeter will take heart from their showing in this competition as they turn their attention to securing a Premiership semi-final spot.
Chiefs head coach Rob Baxter said: "I am disappointed but it was a very good performance and a strong desire to get after the game and do everything we could to win it but we just came up a little bit short.
"It was a big performance, the boys worked very hard and did a lot of really good things. Just one thing would have turned it but that is what happens in big games and I am certainly not going to worry that we lost today."
Baxter was a little frustrated that his side were denied a try in the first half when the Television Match Official Jim Yuille ruled out No 8 Richard Baxter's effort 10 minutes before the interval.
"Everybody this side of the stadium clearly saw that it was a try," said Baxter.
"You have a touch judge this side looking at it who must have seen it as a try yet because they go to the TMO to double check and they haven't got the camera angles and we don't get a try.
"I am going to be very positive about the good things that we did and how we are going to drive those good things over and over again. We played well today and it is a mark of what we can do and really go for things."
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