The Liga leaders squandered a two-goal lead at El Madrigal, Ivan Rakitic and a Neymar penalty giving the club the lead before Cedric Bakambu reduced the arrears and an own goal from Pique's defensive colleague Jeremy Mathieu earned the hosts a point.
Pique was booked after 16 minutes for handball and he handled once more during a challenge on Villarreal midfielder Denis Suarez – an offence that would have ruled him out of next month's Clasico against Real Madrid had it been punished.
"To begin with, the first yellow card was not fair," Pique said, as quoted by Sport. "That ends the discussion. The ball hit me on the chest.
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"For the second one, though, it's true the ball hit my hand, but I had to fall in that way.
"So yes, I admit there's a discussion and a debate, but there's no doubt that if I'm not shown the first booking, we're not discussing all this now."
He added: "It's likely we'd have appealed the first yellow card [in the event of a red] and maybe I'd have been able to play against Madrid. You never know."
The draw edged Barca nine points clear of second-place Atletico Madrid, who suffered a surprise 2-1 defeat at Sporting Gijon on Saturday.
"The victory got away from us, but we managed to get a point," Pique said.
"There are eight games left and we have a nine-point lead. We have to look at things positively."