Giving his reaction afterwards, the replacement out-half said: "You can look to excuses like that if you want but, at the end of the day, we've played enough rugby this year to be able to put a good performance together.
"There were small things like we were a bit loose with our play...certain things and crucial parts of the game didn't go our way. That's what it came down to. I wouldn't put it down to anything like game-time.
"It (coming off the bench) was an opportunity that I would have wanted. When you're on the bench you've got to expect that you can come on at any part of the game. I certainly felt I was ready for the opportunity but unfortunately things didn't go our way in the second half."
Within seven minutes of the restart, Quade Cooper had touched down to give Australia a 22-12 lead and that try proved a key score as it left Ireland chasing the game.
Madigan added: "They did well with ball in hand and in the air. Israel Folau was excellent in the air. Quade was good and found some space in behind us. They just took their chances well.
"The two tries they had in the first half were the (only) two chances they had. We had three or four, we were pushing really hard on the line but came up short."
With World champions New Zealand arriving in Dublin on the back of victories over France and England, Madigan is hoping Ireland can use the disappointment of the Australia game to bounce back against the All Blacks.
"When you lose by 20-odd points it is extremely disappointing. As a professional sportsperson, its a big blow to your ego," said the Dubliner, who now has six international caps to his name.
"We're going to review the game and I'm sure we'll find that there were very fine margins. A pass here, a tackle there and we very easily could have won that game. We're not a million miles off.
"There's still really good belief in the squad. We trained really well over the last three weeks but, unfortunately, things didn't really click for us.
"With Joe (Schmidt) there, we'll have another game-plan to go out and beat the All Blacks. Whatever 15 that are selected will have to go out and do their best to bounce back."
As Ireland wait to hear on Sexton's hamstring injury, Madigan believes it could be a tight call to see who gets the number 10 jersey for next Sunday's final GUINNESS Series game.
"I'm sure it will be (a tight call). I'm not sure of the extent of Johnny's injury, but Paddy (Jackson) played well last week. I'm not sure what Joe is going to do there but it certainly will be a tight call, whatever he decides."