Coleman said Bale, a key figure in Wales reaching the finals of Euro 2016, was going to be included but was left out after conversations with Real.
He has not played a full game for the Spanish club since the middle of last month because of a calf problem, although he could return this weekend.
Ramsey has a hamstring injury, suffered in the Champions League game at home to Bayern Munich a fortnight ago, after which the Arsenal manager Arsene Wenger appeared to criticise Wales for playing him and Bale against Andorra, saying it had "cost" the players.
But Coleman hit back on Wednesday, describing the comment as "a cheap shot".
"Don't comment on Gareth Bale because he's nothing to do with Arsenal," he told reporters.
"And if he's got a problem with my selection or one of his players, like Aaron Ramsey, tell me.
"He called (England manager) Roy Hodgson to speak about Theo Walcott. He didn't call me. Why?
"I'll gladly drive to the Arsenal training ground or wherever his office is.
"If I or my medical staff get no correspondence from a club, that is a green light to play the player.
"Don't point the finger at us. It's not in our interest to gamble with players and we never have done."
(Reporting by Steve Tongue,; Editing by Neville Dalton)
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