Goals from Tottenham's Gareth Bale and Burnley's Sam Vokes put the hosts 2-0 up before Austria pulled a goal back with 15 minutes to go through Marc Janko.
"We scored at a great time in the second half, a great goal from Sam Vokes and a great cross from Bale"
"We got a good performance," Coleman told reporters. "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 Bale.
"We changed Bellamy at half-time and Bale 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.
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"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.
"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."