The Spaniard was shown a straight red card on the hour mark at Estadio de la Ceramica following a reckless studs-up challenge on Sergio Busquets, with the score still goalless.
That marked the turning point in the match as Barca took advantage of the numbers, with Luis Suarez and Lionel Messi going on to wrap up victory to keep the Catalan giants five points clear atop the La Liga table.
"The red card happens within the context of the match. I think the player himself has realised that it was disproportionate to tackle like that,” said Valverde.
"I have not seen the replay, but I thought it was a strong challenge. The player himself was worried and didn't protest.
"I understand he was going to play the ball but lost control. It was a hard tackle and the referee saw it that way.
"[Villarreal] were very well organised and closed up our corridors of attack. It was a game where we were questioned, and we answered."