The Wimbledon champion had beaten Federer at Melbourne Park 12 months ago in the semi-finals but failed to repeat the feat at this year's tournament. Despite saving two match points to force a fourth set, Murray went down 6-3 6-4 6-7(6) 6-3.
After going under the knife four months ago and playing only two competitive matches before arriving in Melbourne, Murray came up short against Federer, who played outstanding tennis in the opening two sets.
"It's frustrating because you put in a lot of hard work for this long period," said the Scot.
"This time I had a long time to prepare, maybe just not enough matches."
But Murray was proud of the way he fought back, breaking Federer when he served for the match at 5-4 in the third set and then saving two match points in the tiebreak to extend the match.
"That's the highest level I've played at in a long time," he said. "My serve slowed down a bit in the fourth set, especially the first couple points when I was getting up after the change of ends.
"But I hung in well. I pushed through it, almost got myself back in the match."
Murray admitted 17-times Grand Slam champion Federer was too good in the opening two sets as he rushed to the net and forced a number of uncharacteristic errors from the Scot.
But the 32-year-old Swiss got tight when he tried to serve it out in the third and Murray, playing more aggressively, fought back superbly to take the tiebreak 8-6.
After holding on in a 19-minute game early in the fourth set, Murray was finally broken in the eighth game and Federer held from 0-30 to clinch his place in the semi-finals.
Despite the defeat, Murray said he was confident he is on the right track after surgery.
"I don't know how many players have come back from surgery and won the first Grand Slam back, in their second tournament," he said. "It's very unlikely to happen.
"I just need to use this as a stepping stone to getting better and be happy that I've got through five matches. The last two were particularly tough.
"I'm playing at a decent level fairly quickly again. Hopefully I'll be back playing my best tennis soon."
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