Gerard Moreno's snap-shot from the top of the box cancelled out Cristiano Ronaldo's penalty in Madrid and although the home side finished the match with 22 shots to Villarreal's six, they could not find a winner.
Pepe was impressed with how Villarreal defended and labelled the visitors "a very good team".
"We wanted to win but Villarreal fought a lot and they ran themselves into the ground," the 32-year-old said, according to AS.
"We fought and we came up against a very good team; we have to keep fighting. We're still top and we have to keep working until the end of the season."
Pepe claimed Villarreal blocked up the middle of the pitch with their 4-4-2 formation.
"We put in a lot of crosses and they had two lines of four, so it was practically impossible to get through in the middle," he said.
"We conceded a goal on a counterattack but that's football."
The draw left Real on 61 points at the top of La Liga, just two points ahead of second-placed Barcelona, who defeated Granada 3-1 on Saturday.
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