Denney, whose high snap against the Jets led to a missed 21-yard field goal attempt by Olindo Mare, bounced a snap to punter Donnie Jones late in the first quarter of Sunday's game.
Jones was able to scoop up the ball, but he quickly lost control of it and Buffalo recovered at the Dolphins 45-yard line.
The turnover led a touchdown that gave Buffalo a 17-0 lead.
"I have total faith, trust and confidence in the guy," Saban said. "He's going to be a long-snapper for a long time in this league."
Saban also said the decision to keep Denney over Perry was made with the future in mind and that Denney would have been claimed off waivers had the Dolphins let him go.
When asked whether he was second-guessing his decision to go with Denney, Saban replied, "You (the media) can second-guess all you want; I'm not going to."
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Saban indicated that the Dolphins' players of the game were Marty Booker on offense; Keith Traylor and Zach Thomas on defense; and Travis Minor on special teams.
For the first time since the opener, the Dolphins didn't rotate their offensive tackles, but it was Stockar McDougle and not Vernon Carey who played the whole game at right tackle. Saban, who insisted again on Monday that the Dolphins basically have three tackles, said McDougle was playing well enough that he didn't feel the need to rotate.
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Wide receiver David Boston, who was inactive against Buffalo, was sent to the doctor to have his ailing knee checked out. Saban said Junior Seau (calf), Eddie Jackson (hamstring) and Eddie Moore (knee) all are day-to-day because of minor injuries.