"And, you know, I think during the last Clinton presidency, the White House did not demonstrate that in a way that was helpful to our nation's culture," Romney added.
New York Sen. Hillary Clinton, wife of former President Bill Clinton, is the frontrunner for the Democratic presidential nomination.
Romney went on to say that the president is under a "microscope," making it especially important to "live by higher standards."
"Because the world is looking at you, you're representing not only yourself but your country," he added. "The kids or America are looking at you. One piece [of instilling values] is acting the part, acting the part of higher ethical standards."
Responding to Romney's comments, top Clinton adviser Howard Wolfson said, "Hillary Clinton needs no lessons on character from a man who switches his positions on a daily basis."