Goals from Gareth Bale and Sam Vokes earned Wales a confidence boosting victory ahead of next month's World Cup qualifying double-header with Scotland and Croatia.
Coleman was happy with his side's performance as he recorded his second win in charge as manager.
"We got a good performance," said Coleman. "First half, I thought we played on the counter a little bit and we went after them also and we had some good chances, but I felt they were making too many chances also it was very open.
"So we got our goal and it was the first time we had gone in at half-time in the lead so we were buoyant and we scored at a great time in the second half, a great goal from Sam Vokes and a great cross from Baley [Bale].
"We changed Bellers [Craig Bellamy] at half-time and Baley after an hour and the dynamics of the team changed, but the lads stuck in there.
"Second half we ground it out, it was more of just get the result. It's a win and they have been hard to come by so we are delighted and I am delighted for the players.
"First half we had some good bits of play and so did Austria, they are a good team, very offensive and quite an exciting team so second half we mainly invited it too much and invited them to hit long balls.
"That's because we were in front 2-0 and then we concede one after 75 minutes and the next 15/20 minutes is a long time in football, but I just thought the players tonight they really dug in.
"We have got one or two players who have not been playing regular, Joe Allen has not been playing regular, Sam Ricketts has been in and out and there are three or four players there who have not been playing regular 90 minutes and then they get tired so we had to make a few changes.
"I was glad to see Joe Allen got the 90 minutes and he did a good job for us, really dug in there. He was getting tired, but he really worked hard and we had two or three players like that.
"We got stretched once or twice, but overall I thought they dug in really well.
"They have been brilliant the last three days, it is nice to have Craig Bellamy back and it's great to get a win."