The 25-year-old excelled during the tournament in France, though he was suspended for Thursday's (AEST) semi-final defeat to Portugal in Lyon.
Ramsey is now set to take a holiday before returning for pre-season duty with Arsenal at the beginning of next month, giving him just less than two weeks to recover fitness before the Gunners' opening Premier League game against Liverpool on 15 August.
Arsenal boss Arsene Wenger gave extended leave to Germany trio Lukas Podolski, Mesut Ozil and Per Mertesacker after their World Cup triumph two years ago, and Ramsey believes he is in much the same position.
"I am back on 1 August, so I have a few weeks off but, obviously, it kicks off a couple of weeks afterwards," he said. "A few years ago, Germany won the World Cup and the German players came in just a few days before the first game of the season, but they missed that.
"He [Wenger] does like to give players a little break and I'll be getting the same treatment. I feel I need a few weeks off now."
Although Wales' historic campaign ultimately ended in disappointment, the former Cardiff City man is glad to have impressed in France.
"Before the tournament, I was really keen to do well and stand up and be noticed," he said. "I feel that I've done that.
"It helps playing in this team, as well, but I wanted to personally do my best and I think I have."