The 25-year-old was booked for a dive in the first half after appearing to be brought down by Burnley goalkeeper Tom Heaton in the box.
"It was a penalty," the Daily Mail quotes Mourinho as saying. "The linesman made a mistake. We have all explained to [Costa] what we want and what people in the Premier League like and don't like.
"We want it calm with fantastic attitude, competitive but clean and polite. The kid was obviously frustrated to be booked and I hope he doesn't get any more unfair decisions."
Chelsea's next game is against last season's Championship winners Leicester City at Stamford Bridge this Saturday.