The former Arsenal man faces a lengthy ban following two separate incidents at Eastlands on Saturday against his old club.
First, the Togo international stomped on Robin van Persie's face after a challenge and later, after he scored, sprinted to the other end of the pitch to celebrate in front of visiting Gunners fans and inciting them.
Scudamore says Adebayor's actions had a negative effect on the league and is confident things will be dealt with properly.
"We've had a fantastic two days of football, and that includes the game at Eastlands," he said.
"Why then, when you run the Premier League, would you want the headlines on Sunday through to Monday being something else?
"You don't want it, do you? So clearly it doesn't do any good for the brand that is football in one sense. You'd rather it didn't happen.
"Of course when these instances come up you'd rather that the talk was about the action and the goals.
"I trust the FA to deal with it and they will do whatever they have to do.
"But these instances, whether they're on the field and beamed around the world like this one, or isolated instances of bad behaviour off the field, don't do the image of the league or football in general any good."