The hosts took the lead after 23 minutes through David Lopez, but Barcelona showed their true mettle in the second half to score two quick goals kind courtesy of Luis Suarez and Arturo Vidal’s strike.
The Blaugrana were cruising to victory before the Dutchman was sent off on the 74th minute mark.
China forward Wu Lei scored the equalizer to deny Valverde’s men the chance to move two points ahead of Real Madrid, who comfortably won against Getafe earlier in the day.
Valverde lamented their inability to kill off the Periquitos and insists De Jong’s dismissal was very crucial.
"We have to fight in every match," the 55-year-old told reporters.
"We started badly, we managed to come back but unfortunately we went down to 10. They pressed and equalised.”
"Frenkie's dismissal did us a lot of damage. We were unable to score a third. This is football.”
"It was a very competitive game, a derby with a lot of tension and emotion. If you're winning and the opponent equalises, you leave with the impression of having lost two points."
He added: "It leaves a bad taste because we wanted the three points,"
"We went in front and it feels like you've achieved a point if you equalise at the end.
"If you concede a late equaliser, it feels like you lose two points.
"We played a match to try to win, It was difficult to break them down, but bit by bit we did it.”
"However, we were left with 10 men and they equalised."
