Peverley/By S. Bradley

BOSTON — No one’s telling Rich Peverley he has to go out and score as many goals as Nathan Horton normally would over the rest of the Stanley Cup Final any more than they’re demanding that of Michael Ryder, Tyler Seguin or any other Bruins forward.

However, Peverley knows that he can play much better than he has lately, even if that doesn’t translate to a Horton-like goal total.

“You want to be able to step up. He’s a tremendous player, obviously,” said Peverley this morning after the morning skate at TD Garden in preparation for tonight’s Game 4 of the Cup Final. “You can’t fill his shoes, but whatever you can do you try to help the team.”

Through 21 games in the postseason, Peverley has produced 2-7-9 totals after he scored four goals through the first 23 regular-season games of his Bruins career. His last goal was in Game 5 of the Eastern Conference Final against Tampa Bay.

In 2009-10, Peverley was among Atlanta’s leading scorers with 55 points (22 goals) in 82 games, so he’s shown an offensive bent that could benefit the Bruins.

He knows he can make up for at least a little of Horton’s absence.

“I think I’ve played OK. I’ve been bounced around a lot of lines,” he said. “The first two rounds was pretty stable, but since then I’ve been working with a lot of different people. I’m not going to say I’m satisfied because I still think I can play a lot better.”

That line bouncing is something Peverley says he’s never done in the past. Despite the lack of goals, he’s been pretty effective at it — serving as a playmaker and even a guy that can get in on the forecheck and keep pressure on the opposing defensemen. He’s just lacked finish, as evidenced by his 12 shots on net in the last eight games.

Whatever line or lines he winds up on tonight, Peverley’s going to try to make an impact.

“It’s still something that you don’t want to change your game too much,” he said. “You’ve just got to continue to go out and use your assets.”