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On Friday, the Jordanian Al-Qadi family bought a 92% stake in the promotion-chasing League Two team.
Rovers sit sixth in the table after coming from behind to beat Morecambe 2-1 on Saturday.
"If they want to sack me, they want to sack me, but as it stands at the minute the owner's fully behind me," Clarke, 38, told BBC Points West.
"I don't fear for my job - why fear for my job? As soon as you're a manager and you start fearing for your job, you're out the door.
"What I will say is that I have it a certain way. I'm the manager, I pick the team, I pick the players that come into the club and the new owners are embracing that."
The Pirates are five points outside the League Two automatic promotion places, having secured their return to the Football League last May.
But Clarke, who replaced John Ward as Rovers manager in March 2014, said he did not find out about the takeover until the morning the deal was announced.
"We never knew about a takeover," he said. "You hear rumours and all the bits and pieces, but we found out about this on Friday morning and I'm supposed to be preparing my team.
"It's great what the owners have been saying and how the club's going to move forward, it's great for the supporters. But on the back of that, I've got to manage that.
"I've got staff who are thinking: 'Well, what's going to happen with my job?' You've always got people that are concerned about their jobs."

The eighteen-year-old lost his lower legs and spent nearly a month in hospital after the accident.
It happened during a race at Donington Park, days before his birthday.
When he was recovering from his accident, Billy said he really wanted to race again, despite his injuries,
Now the Formula 4 racer is back behind the wheel - trying out a car specially designed to make it easy for him to drive.
The controls for the Fun Cup endurance racer are attached to the steering wheel instead of being the floor of the car, where they'd normally be.
The new racing car came from a group called Team BRIT. They help disabled people and people with injuries that would making driving difficult, to compete in motorsport.
It's designed to look like a Volkswagen Beetle, and Billy's been giving it a test drive at Brands Hatch in Kent.
Billy says it's been really good just to get back behind the wheel, but he still wants to perfect his technique and get used to driving the new car.
While Billy still has some training and therapy to get through, he says that's all going well, and he's hoping to get back out on the track properly soon.
He says his ambition is now to compete in the Le Mans 24 Hours, along with Frenchman Frederic Sausset, who lost both his arms and legs through an illness.
The teenager also wants to thank his fans, saying he's been overwhelmed by the help they've given him.
He says: "People keep saying I'm the inspiration but I think all these people coming together to support someone who has gone through an accident like this, they're the true inspiration."
Bristol Rovers boss Darrell Clarke says he is not worried about losing his job following the club's recent takeover.
[NEXT_CONCEPT]
Teenage racing driver Billy Monger has returned to the racing track, almost three months after he was badly hurt in a crash.