“We’ve got other players to step in and do the job for us, which they will do.
“But Joe won’t be available. With the problem he’s got you could play him or train him and it could go any minute.”
Coleman hopes Allen will be fit when they host Serbia on Saturday, 12 November in Group D.
“We really need him next month. So from between now and then what he does is going to be very important,” said the Wales boss.
“Whether he comes back too soon for Stoke, hopefully he won’t. I’m sure they won’t take a chance with him.”
‘No excuses’ against Georgia
Wales remain top of their group on goal difference but level on points with second-placed Serbia, while Austria and the Republic of Ireland – who beat Georgia 1-0 – drop to third and fourth respectively.
Coleman added: “Have we got enough to get a result on Sunday without Joe Allen? Yes, we have. So I won’t make any excuses.”
The Wales manager says he could “probably have gambled” and kept Allen on the pitch.
“But we don’t want to be doing that. He had a twinge in his hamstring, so that’s why we took him off immediately,” said Coleman.
“Joe belongs to Stoke City and we have to send him back in the condition that we received him. That’s why we he came off.”
Bale: Wales ‘frustrated’, but defended ‘solidly’
Midfielder Gareth Bale said Wales were “frustrated”, but underlined their qualities to win a point in Vienna.
“It’s a difficult place to come if you look at their record in qualifying,” said the Real Madrid player.
“They didn’t lose at all [in qualifying for the Euros] and drew one game.
“We know we weren’t at our best tonight. It was a difficult game. They’re a very good team.
“This is what we’ve grown up to do – we grind out results when we need them.
“When we don’t play well we defend solidly as a team. We get something from the game.
“We were frustrated. We know we didn’t play well enough tonight.”