Coleman's position is under scrutiny after last month's defeats to Macedonia and Serbia led Football Association of Wales chiefs to stall over a two-year contract extension until after the end of the Group A campaign.
Coleman's irritation with the situation has been clear to see and he has demanded the full backing of the FAW if he is to continue, while admitting the association has asked him to change his backroom staff.
But the fourth victory in his 14-match reign, which came thanks to a committed effort from a patched-up side after 11 players withdrew from Coleman's original squad, will have at least alleviated some of the pressure on him.
And the Wales boss said: "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."
Wales could have enjoyed a more comfortable margin of victory had the otherwise excellent Aaron Ramsey not failed to convert a penalty after Church's opener, but they still climbed off the bottom of Group A above Macedonia and Scotland and into fourth place.
But Coleman insists the result will have no influence on any decision he has to make over his future.
He said: "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.
"But 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 and I am not looking beyond that."
Victory over Macedonia ensured Craig Bellamy's final home game in a Wales shirt ended on a positive note and Coleman praised the 77-cap forward's performance as part of an inexperienced squad.
"Craig was magnificent like everybody else," said Coleman.
"We switched him to the left to look after Declan John on his first cap and he did a great job."
Macedonia coach Zoran Stratev felt his side had failed to make the most of their chances.
He said: "We had more possession but we did not take any of our opportunities and this Welsh side knew how to punish our mistakes."
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