The wide receiver was taped up during the postgame news conference, having looked to have rolled his ankle in the fourth quarter of his side's 14-31 loss, sparking fears of a potential lay-off.
But Kupp is optimistic he has not done serious damage as he waits to discover the extent of his injury.
"It just got rolled up a little bit," he said. "[My] foot got caught, but I think it was able to slide out of there before there was too much damage done.
"So, we'll see over these next few days how it responds. Right now, things are pointing towards dodging a bullet."
Rams head coach Sean McVay felt he should not have put Kupp - who made eight catches and scored a touchdown - in the position to suffer the injury in the first place.
The 29-year-old has no issue with his boss, stressing that such an injury is simply the nature of the game.
"Beyond just the coach that he is, he cares about his guys and about his players, and so I know he feels bad about that," he added.
"But at the end of the day you're playing a football game. So I obviously don't hold anything against him in that regard.
"It's a violent random game, and you play it as hard as you possibly can until the fourth quarter hits zero. And I can respect that and appreciate that."