Pence also didn't criticize the show's cast for addressing him from the stage after the play's end Friday night, saying he wasn't offended and understood their message.
"I did hear what was said from the stage. I can tell you I wasn't offended by what was said. I will leave to others whether that was the appropriate venue to say it," he said on "Fox News Sunday."
Pence's comments come after Donald Trump's Saturday morning Twitter attacks
on "Hamilton," accusing the cast of harassing Pence.
"Apologize!" Trump demanded in one tweet.
Trump resumed those complaints Sunday morning, tweeting: "The cast and producers of Hamilton, which I hear is highly overrated, should immediately apologize to Mike Pence for their terrible behavior."
Trump's tweets have amplified the comments from a cast member, read on-stage after the production.
Brandon Dixon, who plays Aaron Burr in the hit musical, began the message by thanking Pence for attending the play and saying, "We hope you will hear us out."
"We, sir -- we are the diverse America who are alarmed and anxious that your new administration will not protect us, our planet, our children, our parents, or defend us and uphold our inalienable rights," Dixon said. "We truly hope that this show has inspired you to uphold our American values and to work on behalf of all of us."
Pence addressed those comments on "Fox News Sunday."
"I do want to say that the basic element, the center of that message is one I want to address and that is I know this is a very disappointing time for people that did not see their candidate win in this national election," Pence said.
"I know this is a very anxious time for some people. I just want to reassure people what President-elect Donald Trump said on election night -- he absolutely meant from the bottom of his heart," he said.
"He is preparing to be the president of all of the people of the United States of America and to watch him bringing together people of diverse views, bringing people together who disagreed with him strongly, seeing him talk to leaders around the world. I just want to reassure every American that in the days ahead I am very confident that they are going to see President-elect Trump be a president for all of the people and we embrace that principle. We are going to work hard to make that principle every day that we serve."
The "Hamilton" cast's message to Pence came after some in the crowd booed the Vice President-elect.
Pence said he did notice the booing, but it didn't spoil the show.
"My daughter and I and her cousins really enjoyed the show. 'Hamilton' is just an incredible production, incredibly talented people. It was a real joy to be there," Pence said.
"When we arrived we heard a few boos, and we heard some cheers," he said, "I nudged my kids and reminded them that is what freedom sounds like."