The Blues were held to a goalless draw at Stamford Bridge by their London neighbours, again struggling for goals.
Aubameyang was completely omitted from the match day side, as Potter welcomed five January signings into the squad.
The Chelsea manager revealed it was his decision to leave the striker out of the picture.
He said: “It was my decision and it was tough decision, but sometime you have to make those calls.
“Someone had to miss out. He’s done nothing wrong at all. I’m empathetic. I understand his disappointment.
“He reacted in the right way. He trained very well today.”
Aubameyang, 33, was brought over to Chelsea from Barcelona by Thomas Tuchel.
But after Potter replaced Tuchel in September, the former Arsenal captain has struggled for game time.
Aubameyang has been linked with a move away and his future appeared further in doubt after he flew out of the country.
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The forward was pictured in Milan – where he spent four years as a player – with his family.
Asked if Aubameyang had permission to fly to Milan, Potter added: “He’s got the weekend off. It’s a free world.”
Mudryk started on the left at Stamford Bridge but was taken off at half-time – having suffered from a COLD.
Potter said: “He had a heavy cold all week.
“We thought 60 would be his maximum but he just felt heavy legged at half-time so felt 45 was right for him.”
Chelsea’s draw takes them up to ninth, but Liverpool have two games in hand over them.