Riley opened his season-ending news conference Thursday saying that he was angry about what he calls a lack of perspective about the Heat, who have been to the NBA Finals in each of the last four seasons and won two of the last three championships.
"You want to trend something?" Riley asked reporters. "I'm pissed. Get that trending."
James, Wade and Bosh can all opt out of their current contracts and become free agents this summer. They each have two seasons and at least $40 million remaining on the contracts they signed in 2010.
"I think all those guys that have come here have got exactly what they wanted," Riley said of his Big Three. "And we hope that all those guys want to come with us. What cements a forever-bond is going through what we went through this season and staying the course."
He also thinks that the Heat shouldn't get too down because they didn't win a third consecutive title.
"You got to deal with it. You've got to come back," Riley said. "This stuff is hard, and you've got to stay together if you've got the guts. And you don't find the first door and run out of it.
"We need to retool. We don't need to rebuild. But everybody get a grip. It's been a great run."
The Associated Press contributed to this report.