"We're fine," the Indiana governor told CNN's Alisyn Camerota on "New Day" during a phone interview. "It was about 10 seconds of uncertainty last night, but we're just so grateful to the pilots and to the first responders on the scene and (that) everybody came off the plane safely."
None of the 48 people on board were injured in the rough landing.
Pence said he felt plane fishtail after it landed during a rainy evening in New York, but added that he kept a saying from his son, who is a Marine Corps aviator, in his mind following the incident: "Every landing you walk away from is a successful landing."
The press pool in the back of the aircraft, a Boeing 737-700 chartered from Eastern Airlines that was painted with the campaign's logo, could also feel the plane fishtailing as it touched down and slid off the runway before coming to a very sharp halt in the grass off the side of the runway.
Once the plane came to a full stop, the Indiana governor walked to the back of the plane to check on the press. As everyone on board deplaned, Pence could be seen speaking with emergency responders.
A spokesman for Pence said the vice presidential nominee retired to his hotel for the evening, canceling an appearance at a closed-door fundraiser that had been scheduled in Trump Tower. He called into the event instead, a senior Pence aide said.
Stephanie Grisham, a spokeswoman for Donald Trump's campaign, said the businessman called Pence shortly after the incident, adding that Trump "is very glad everyone onboard the plane is safe."
At the time of the incident, Trump was in Ohio, where he later addressed a rally in Geneva and briefly referenced the close call.
"I just spoke to our future vice president, and he's OK. Do you know he was in a big accident with the plane?" Trump said. "Everybody's fine. But what a great decision it was to get Mike Pence. What a great guy he is. What a great job he's doing."
Pence was due to campaign in Pennsylvania and North Carolina on Friday, and the campaign said his schedule would go forward as planned.
Following the incident, Pence tweeted, "So thankful everyone on our plane is safe. Grateful for our first responders & the concern & prayers of so many. Back on the trail tomorrow!"
Hillary Clinton offered her regards via Twitter as well, writing, "Glad to hear @mike_pence, his staff, Secret Service, and the crew are all safe. -H"
Rescue crews quickly responded on the scene, where there was some noticeable damage to the runway, although a campaign spokesperson told reporters there was no structural damage to the plane. A law enforcement source told CNN the damage to the runway was due to safety material at the end of the runway that is designed to break apart.
Dray Clark with CNN affiliate WABC
tweeted video of the plane's front wheel being lifted out of the ground early Friday morning.
The Indiana governor's return trip to New York had initially been delayed due to inclement weather. His plane was kept in a ground hold at the airport in Fort Dodge, Iowa, earlier in the day.
Pence took advantage of the flight delay to toss around a football with members of his staff and threw a few easy passes to the press.
Mary Schiavo, a former inspector general for the Department of Transportation, explained to CNN's Anderson Cooper that the weather likely prevented the plane from getting "good traction."
"When there's a layer of water on it, it is very much like hydroplaning in your car," she said, adding, "LaGuardia has had this very thing happen before."
A spokesperson for the Federal Aviation Administration told CNN it will be investigating the incident. A US official told CNN the National Transportation Safety Board was gathering preliminary information on the incident and will launch a team to investigate Friday morning.
The Port Authority of New York and New Jersey issued a statement confirming no one had been injured and that its personnel were on the scene. Planes were temporarily prevented from landing or taking off at the Queens airport, though the FAA later reported that departures and arrivals had partially resumed on one runway. Delays were expected to continue, the FAA said.