"As I travel the country here in Iowa, New Hampshire, South Carolina, Nevada, everyone knows what New York values are," Cruz told ABC News White House Correspondent Jonathan Karl minutes after delivering his victory speech. "It's the values of the elite liberals that have done enormous damage to New York and they're a bunch of cops and firemen and hardworking men and women in the great state of New York who are fed up with the out-of-touch values of Manhattan.
"This is a center-right country. The values of this country are reasonable, common sense. Their Judeo-Christian values are the reason our campaign is resonating and resonating among Reagan Democrats in particular is because getting back to the principles that built America and those principles bring us together."
Cruz maintained he would not "insult" the real estate mogul-turned-presidential candidate, but instead was willing to point out how they differ on policy matters.
"I will praise Donald Trump. He's bold, I think he's brash, I'm glad he's running. He's energized a lot of people," Cruz said. "Now, I'm willing to draw differences on policy. Policy is fair game."
The Texas senator basked in his win over Trump in Iowa, calling it "an incredible victory for the grassroots."
"This victory was won friend to friend, neighbor to neighbor, Iowan to Iowan. That’s exactly the approach we are taking now to New Hampshire, South Carolina, to Nevada," he said.
Recent first-place GOP finishers in the Iowa caucuses have not fared well further along in the nominating contest. The two previous Republican Iowa caucus winners – Mike Huckabee in 2008 and Rick Santorum in 2012 - failed to clinch the Republican presidential nomination.
But Cruz said he’s different, pointing to his fundraising prowess and organizational capacity as examples for how he could win the nomination.
"Both of them came out of Iowa broke. They did not have a national infrastructure, they didn't have the team in place to be able to compete effectively enough to win the primary," Cruz said. "We're in a markedly different situation.
"We're running a national campaign. And if conservatives continue to unite I believe we're going to win this nomination and win the general election in November," he added.
Asked whether he’s going to win the New Hampshire primary, Cruz said, "That's up to the people of New Hampshire. We're going to compete for every vote in that state and I hope to earn those votes and earn their trust."