He will now miss Wales' World Cup qualifier against Croatia on Tuesday and he acknowledged he needs to learn from the incident after saying sorry to coach Chris Coleman.
"It was very disappointing - it's something I need to learn from," said Ramsey.
"I should have looked up at the clock and let the goalkeeper take the free-kick. I had to (foul McArthur) in the end.
"It's disappointing to do what I've done after a great performance.
"I said sorry (to the manager) for letting the boys down. I'm missing the next game so I apologised."