The MTV star says he's always made it a point to live an honest life and own up to his past mistakes

Nev Schulman is doing his best to move on after facing allegations of sexual misconduct on his hit show Catfish: The TV Show.

In June, MTV closed an internal investigation after a woman who previously appeared on the show accused Schulman of making inappropriate and sexual comments toward her while filming. MTV said the claims were found to be “not credible and without merit.”

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“I’m doing much better now,” he tells PEOPLE. “It was a really difficult time for me, as much for my wife and my family. It was tough.”

Schulman says he’s always made it a point to live an honest life and own up to his past mistakes.

“I’ve lived a number of different lives in my 33 years. I’ve experienced different things, I’ve been in different social circles and I’ve made mistakes. I’ve been very honest about those and I’ve been accountable, I’ve apologized and done everything I could to make right where I may have wronged. I’ve been judged for those mistakes — publicly and privately. That’s tough and doesn’t feel good but it’s important and something I’ve made part of my life.”

Image zoom Nev Schulman FilmMagic

He says he tries to live by the same morals and values that are represented on Catfish: accountability and honesty.

Schulman says he felt “powerless” as the investigation was underway.

“To be accused of something that I squarely did not do and to have the harsh judgment that followed and no way to counteract or do something in the moment to correct that was very difficult,” he says. “It was frustrating. I just felt so powerless.”

When the accusations were first made public in May, Schulman says he was “overwhelmed” by the amount of support he received from fans and past participants on the show.

“Luckily I had the amazing support of the fans of the show but also of my colleagues, the crew,” he says. “Several people who had been on the show actually reached out to me and offered to speak up in my support if necessary. I’m just so thankful and grateful to everyone.”

In May, Schulman denied claims of sexual misconduct made by a woman who appeared on the show.

“The behavior described in this video did not happen and I’m fortunate that there are a number of former colleagues who were present during this time period who are willing to speak up with the truth,” Schulman said in a statement to PEOPLE. “I have always been transparent about my life and would always take responsibility for my actions — but these claims are false.”

While Schulman, 33, does not name his accuser, fans believe he is referring to a YouTube video posted by a woman named Ayissha Morgan, who appeared on season 4 of Catfish in 2015.

Morgan alleged on May 12 that show’s “main person” made inappropriate comments to her.

“On every break from filming, every time they said cut, they’re like, ‘Oh, well when can I take you on a date?’ Mind you, this was 20 minutes in from us meeting for the first time,” she said in the video. “I was in such an uncomfortable place and a freaking hard time in my life as well. I’m at my most vulnerable.”

Morgan could not be reached for further comment.

Schulman serves as the host and executive producer for the popular MTV show, which investigates online relationships and exposes people who impersonate others on the internet — and is based on his 2010 documentary.