"(We are) having to play each other in the third round, one of us is going to be gone", Serena said.
"She looked like she never lost a step", Venus said of her younger sister.
"Obviously, I wish it was anybody else in the draw, literally anybody, but that's OK", Serena said.
The sisters were supposed to clash in the 2001 semi-final here, but Venus withdrew only a few minutes before the match was to begin, citing tendinitis in her right knee.
Ekaterina Makarova of Russian Federation led 10th-seeded Angelique Kerber of Germany 6-3 when their match was stopped in the opening game of the second set with Kerber holding a break point.
And the 36-year-old backed that up with a battling display, which lasted nearly two hours against the spirited Dutchwoman, despite tallying 34 unforced errors.
"My comeback could not have come on a better day and I decided I wanted to do something different let you all be a part of my long journey back", she added.
Spectators vented their displeasure with the withdrawal during the final, booing Serena and jeering her sister and father Richard Williams when the pair arrived to watch the match.
The 36-year-old Serena took centre stage as she needed just under two hours to dispatch Bertens, of the Netherlands, 7-6 (7/5), 7-5 here, Saturday.
Still showing some rust from her long layoff, Serena hit just one ace and made 37 unforced errors to 32 for Bertens.
Talking to the audience and press after the game, Williams shared her thoughts over her impressive win against Diyas.
"She's had such a good year last year and playing fantastic tennis".
"I think it's a huge difference to play her in the semifinals or even the quarterfinals or a final as opposed to a third round", Serena Williams said.
"But I have to play a seed regardless, sooner than later most times for the next couple of tournaments". "When she's missing, it's not by much".
The American who already has two Indian Wells title is vying to become the first woman to make it three here clinched her victory on the second match point when Bertens blasted a forehand as she broke the Dutch's serve six times.
"(I was) just trying to work the point, do what it takes to win the point.
She fell behind 3-1 early in the second set but rallied by holding serve in the fifth game.
"It definitely felt better than the first round, but I'm still a little rusty".