The Clippers have often come second best to their city rivals over the years until last season, when they recorded the fourth-best win percentage in the Western Conference while the Lakers struggled.
However, Rivers believes that his side need to ge better in the playoffs if they are to call their relationship with the Lakers a genuine rivalry.
The former Boston Celtics coach told reporters: "The Lakers have been pretty dominant. We've won as of late. It's going to take us a lot more to call it a rivalry, honestly.
"We have to do a lot more stuff and then we can call it a rivalry. I don't think we've done enough yet.
"[The Lakers] have won a lot in the playoffs. They can say that. We can't. It's tough for me. I got to give them that respect. That's the respect we have to earn. They've already earned that through history. We haven't. That's something we have to earn."
The two sides meet at the Staples Center later tonight.