Bale returned from suspension at the Principality Stadium after missing the 1-1 stalemate with Serbia in June, the fifth time in sixth qualifiers Wales had been held to a draw.
Woodburn's victor against Austria revived Wales' World Cup qualification hopes, cutting the gap to the Republic in second place to two points and four to Group D leaders Serbia.
"Jurgen Klopp felt it was a bit early for Ben but we've all got opinions which is what is great about football", said the Wales boss.
Wales struck twice in the final 10 minutes to record a hard-fought 2-0 victory over Moldova and boost their World Cup qualification hopes.
Threatening, albeit from distance, the visitors saw several chances spurned, the best falling to Arnautovich who should have done far better with his opportunity, and it was Chris Coleman's men who were the more relieved to go in at half-time level.
Martin O'Neill's Ireland dropped two points behind Serbia, who they host in Dublin on Tuesday, while Austria's prospects now appear all but doomed ahead of the visit of Georgia.
Speaking to the media last week, Coleman recalled the horrors of that Moldova trip but he's confident that it will be a different story for his team - on and off the pitch.
"It does make me feel old - I'm 11 years older than him", Bale said. "It doesn't compare to where we stayed in 1994". It was unbelievable. We had cockroaches too. It was unbelievable. The country was in a lot of trouble at the time.
The message from Chris Coleman to his players at half time would surely have been for them to remain patient, and try to move the ball slightly quicker, and ultimately it paid off.
"This is a hard game but, like in basketball and hockey, you focus on the next win - and that's what we will do".
"You could put him in any position and we would rise to the challenge, he's that motivated".
"That was what was running through my mind when I came on". We let Wales down. We felt so flat going into that game but I should have known that Scotland always produce when they're down on themselves.
The Wales players applaud their fans after the match.
"Most importantly, we got the three points and are still in with a good chance of doing something".
But, if next month's mouth-watering home clash with Ireland is to mean anything to Wales, nobody should be taking anything for granted.