Data from flight tracking website RadarBox suggests the aircraft struggled to reduce its speed upon landing, reporting the plane was travelling at a speed of 110 knots (204km/h) on the final third of the runway.
Panicked passengers were evacuated from the aircraft early on Sunday after emergency service crews arrived at the scene.
One unnamed passenger told Turkish media they waited inside the plane "for at least 20 minutes" waiting for help to arrive.
"There was a smell of fuel inside so we all thought the plane [would] explode, but thankfully it did not happen," they said.
Another passenger, Fatma Gördü, said there was anguish amongst passengers on board after the plane landed in rainy conditions, adding the aircraft started "shaking" on the runway.
"We tilted to the side, the front was down while the plane's rear was up. There was panic. People shouting, screaming," she told state-run news agency Anadolu.
Another passenger, Yüksel Gördü, said it was "a miracle" that they survived the ordeal.
"The plane could have caught fire or fell into the sea. I thank God it didn't. I feel like going crazy whenever I think about these moments," he said.
Footage posted on social media showed at least one of the aircraft's windows had been smashed and another clip appeared to show one of the plane's engines in the water.
Trabzon governor Yucel Yavuz said the cause of the accident, which resulted in the airport being closed for several hours, is not yet known.
"We've taken all necessary measures," he told Turkish media. "We will reopen the airport to airport traffic as soon as possible."
Pegasus Airlines said in a statement they were "sorry to report" that Flight PC 8622 "had a runway excursion incident during landing".
"All 162 passengers, 2 pilots and 4 cabin crew have been disembarked safely from the aircraft. There has been no loss of life or injury to anyone on board," the statement said.
Turkish Airlines said two inbound flights to Trabzon and a scheduled flight from the city to Istanbul were cancelled as a result of the incident. All services have now resumed as normal.