"Oh, well. It's good to talk about the bad stuff first, I guess," Federer said sarcastically as the crowd began laughing.
Courier continued putting Federer on the spot, probing him about his mysterious leg injury.
"I've had a leg thing going on for the week. I felt it from the second game on in the match," Federer said.
"And I said 'you know what? I never take injury time, and Stan already took his. People won't be mad, and Stan won't be mad hopefully'."
Federer continued to explain why he had to leave the court, awkwardly hinting the problem may have been a little too risque for the crowd's viewing.
"If you go off the court that means the treatment is further up the leg," the world No. 4 said to a hysterical audience.
"You don't need to be more specific," Courier replied. "That's enough. We're gonna move along."
"But not that specific. We're still talking about the leg right?" Federer laughed.
"These things are getting looser and looser, these interviews," Courier concluded.
Federer scraped home against Wawrinka, admitting the final hour of play was extremely testing as the younger Swiss dominated the baseline.
"It was tough. I felt that Stan had the upper hand in the fifth (set) from the baseline. I felt he was reading my serve well," he said.
"I did feel like he gave me a cheap break. It's not like I really deserved it at that moment but after that I did well and served home. I couldn't be happier right now."
He took the match 7-5 6-3 1-6 4-6 6-3, progressing into a dream final to take a shot at a fifth Australian Open title.
Federer admitted he thought the time may have passed for another Australian Open final against his old foe Rafael Nadal.
The legends last met on a court playing some playing mini tennis with some juniors and discussed playing a charity match.
Instead they may square off in a grand slam decider that many - including themselves - felt was beyond them.
The last time the duo battled in the final at Melbourne Park was in 2009, which the Spanish bull won.
Federer, 35, is returning from six months out following knee surgery while Nadal, 30, had an injury-ravaged 2016.
Federer booked his berth in the final with a gripping 7-5 6-3 1-6 4-6 6-3 win over Swiss compatriot Stan Wawrinka while Nadal must get past in-form Grigor Dimitrov in Friday night's semi-final to complete the fairytale. "It would be unreal, both of us would never thought that we would be here potentially playing in the final again," Federer said after his five-set victory.
"I went to open his academy and I told him, 'I wish we could do a charity match or something', but I was on one leg and he had a wrist injury and we were playing some mini tennis with some juniors, but it was the best we could do. "A few months later we are maybe going into the final; I think it is very special for both of us." The Swiss master, who is gunning for his 18th major title, described himself as Nadal's "No. 1 fan".
"Rafael Nadal has given me the biggest challenge in this game," Federer said. "I think his game is tremendous, he is an incredible competitor. "Of course it would be unreal as both of us would never thought that we would be here potentially playing in the final again."