The United States must remain "deeply engaged" in global affairs to protect its interests and maintain its leadership role as an international superpower, former Defense Secretary William Cohen said Thursday.

Cohen, a Republican who was President Bill Clinton's defense secretary, disagreed with Donald Trump's suggestions at Wednesday night's debate that the United States is doing favors for other countries.

"The fact is that we are in those countries with their consent and with their financial support," Cohen told CNBC's "Squawk Box." "We are extending the perimeter of democratic countries to prevent those who are not democratic from overwhelming them, so it's in our interests to be there."

Cohen, chairman and CEO of the Cohen Group, said that while he disagrees with the Obama administration's handling of the war in Syria, he believes Hillary Clinton presents a sounder solution.

"I support what Hillary Clinton has been saying about the need for a safe zone [in Syria]," Cohen said. "You have to have a place where these poor people can go and feel that they're being protected."

Cohen said that if the United States does not maintain its global role and instead becomes subject to the isolationist and protectionist measures that the Republican nominee supports, the turbulence of the world will only persist.

"We have to remain deeply engaged in global affairs, and if we're not, then I think you'll see comments coming back to us saying, 'you're losing your leadership role, you need to be much more aggressive diplomatically, economically,'" Cohen said.

The way to move forward, Cohen said, is to remain front and center "on the world stage," so that the United States can continue to set the agenda and establish world order.