Austin's goal after 10 minutes was enough for victory in a game Hartlepool simply had to win to avoid the drop.
Hughes still faces mission impossible to keep Pools up but he described his players as '11 heroes' after they hung on at play-off chasing Tranmere.
"It was a great win in terms of effort and commitment," said Hughes. "It was a rearguard action but the penalty gave us something to hang onto and we certainly did that.
"There were 11 heroes on the pitch, plus the substitutes, and we were just happy to see the ball hit the back of the net.
"We showed plenty of desire and that's what it is all about. We gave up a lot of territory and tried to hit them on the counter attack but there is more than one way to win a football match.
"There was plenty of pride evident in our performance and it was such a crucial game. We showed courage and we had to want it more - it was critical. We hung on in there and all credit to the boys.
"We can play better football but it was a must-win cup final if you like and the players certainly came up with the goods."
Owain Fon Williams kept out Simon Walton's penalty but Austin pounced to slide home the rebound.
Tranmere were awarded a penalty of their own 12 minutes after the break but Scott Flinders superbly tipped Andy Robinson's spot-kick onto the crossbar after Peter Hartley was judged to have fouled Jean-Louis Akpa Akpro.