Quinlan was suspended for 12 weeks after he was found guilty of an act contrary to good sportsmanship under Law 10.4(k) during Munster's Heineken Cup semi-final loss against Leinster on May 2.
His appeal today was turned down and the 12-week suspension stands, meaning the Tipperary man will miss the tour to South Africa.
Davies said: "Alan Quinlan's suspension is naturally disappointing and he must be devastated by the outcome of the hearing and appeal.
"That said, the Lions management fully accepts the decisions of the ERC judicial process.
"The outcome necessitated the selection of a new player and Ian McGeechan and his fellow selectors had no hesitation in selecting Leicester's Tom Croft."
"However, following the outcome of the appeal we have replaced Alan with Tom Croft who, it must be said, was very unlucky not to have been selected in the original tour party.
"Tom showed in his recent performances for Leicester, following the tour party announcement, that he could put aside his disappointment and perform at a very high level.
"He was on our selection reserve list and today his continued good form has been rewarded with selection to the Lions squad for the tour of South Africa."
Croft will link up with McGeechan's squad after playing for Leicester in Saturday's Heineken Cup final against Leinster at Murrayfield.