Ramsey was shown a second yellow card following a foul on James McArthur in stoppage-time after he had made a hash of a quick free-kick.
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."
Meanwhile, Ramsey believes the victory over Scotland proves that Wales are not just a one-man team after Gareth Bale was forced off at half-time with his team trailing 1-0.
A Ramsey penalty and Hal Robson-Kanu header earned Wales a second qualifying success and the Arsenal midfielder was pleased with the second-half response.
He added: "We have some very good players who can do things, great things, and are comfortable on the ball. We proved that in the second half.
"Gareth Bale can do something out of the ordinary and that is what teams are wary of. But we showed we have a lot more to offer than just him."