Federer got his Cincinnati Masters campaign off to a flier with a routine 6-4 6-4 win over Gojowczyk last night.
The 37-year-old is currently preparing for the US Open where, having been beaten by Anderson at Wimbledon, he is aiming for Grand Slam No 21.
Roger Federer was dejected after his defeat in London last month having set his sights on making more history at the All England Club.
And the veteran has now admitted he feels good after beating Gojowyzck after having over a month to stew over his Wimbledon exit.
“I felt good in that first match, to be honest, walking out, hardly any nerves. I think I knew what I had to do,” Federer said.
“It’s fast-court tennis. I knew my opponent was going to go for it and take big cuts at the ball, so there is only so much you can really do.
“It’s nice to have played a match so that my last match was not the Anderson match … you’ve kind of turned the page. It’s a good thing.
“The goal is now to recover from this match, take the positives with me. Of course the big goal is the US Open.”
Federer is aiming for a first US Open title since 2008.
Back then, many were expecting his career to wane as he entered the twilight years of his career.
A decade on, though, Federer will grace Flushing Meadows as one of the favourites to scoop the prize.
And, speaking before his Gojowczyk victory, the world No 2 revealed the secret to his longevity.
“It’s important to always try to play your game, especially on faster surfaces, and not be too reactive,” he said.
“In this day and age everybody serves big, everybody can hit big from the baseline.
“So it’s important to bring in your own energy, whether it’s the first round or the finals.”
Federer is next in action against Leonardo Mayer tomorrow.