Coleman had 11 players missing from his initial squad selection, but they managed a 1-0 triumph in Cardiff thanks to Simon Church's strike.
But the Wales boss admitted: "Had we lost this game, I would have been out the door, no doubt.
"It's a win and, for me as a manager, looking at our squad of players and all the pull-outs we had, I am delighted.
"I wanted us to look after the performance and we did that. We may have ridden our luck a bit but I thought we deserved to win.
"I enjoyed the win tonight more than any other because there has been a lot said and we were up against it. The players stood up to the test."
Coleman is in talks with the Football Association of Wales over a new contract, but question marks remain over his future.
"The contract will be talked about but nothing has changed. I am not sure what anyone can do if we haven't got our best players all the time.
"We need all our best players for a lot more of the time than we have had. It would make no difference what manager is sitting here in front of you.
"I don't know what I can do when we haven't got them. I know what I can do when we have them and how we can play.
"But we have come into this camp, with a lot of withdrawals and we have won. We now face a huge test on Tuesday against one of the best teams on the planet in Belgium and I am not looking beyond that."