"We look like Mississippi," the governor told WITN-TV.
Unofficial returns show the amendment - which defines marriage solely as a union between a man and a woman - passed with about 61 percent of the vote to 39 percent against.
North Carolina is the 30th state to adopt such a ban on gay marriage.
State law already prohibited same-sex marriages. Supporters said they wanted to write it into the constitution to further protect traditional marriage.
Perdue, who previously said she was against the amendment, told WITN that the vote is wrong for the state.
"People around the country are watching us and they're really confused to have been such a progressive forward thinking economically driven state that invested in education and that stood up for the civil rights people including the civil rights marches back in the 50's and 60's and 70's," said Perdue. "People are saying what in the world is going on with North Carolina, we look like Mississippi."
"We're not worried about it, to be honest with you looking like Mississippi," said Pastor Patrick Wooden, with the Upper Room Church of God in Christ. "We didn't shoot anybody. We didn't kill anybody. There was no bloodshed. No one was lynched or hung. We voted -- one person, one vote. And the voice of the people was heard. I'm disappointed in the governor."
The governor likened the fight for gay marriage to the civil rights movement, which Wooden finds offensive.
"I've never seen a sign that says heterosexuals enter the front door, heterosexuals go to the back," said Wooden.
Jeremy Kennedy with the Protect N.C. Families Group, which fought against Amendment One, said Perdue's comments say more about the issue than any state.
"You're dealing with people and you're dealing with protections under the law," said Kennedy. "So of course it's a civil rights issue. It's going to be something that I think clear through the November election the entire country is going to be talking about."
Mississippi Gov. Phil Bryant issued a statement in response to the derogatory remarks about his state made by Perdue: "I am certainly disappointed by Gov. Perdue's statement regarding North Carolina's 'looking like Mississippi.' Apparently, North Carolina's voters are much more in line with Mississippi's traditional values on marriage than those of Gov. Perdue."