Belgium international Courtois became one of only five goalkeepers to achieve a hundred or more shutouts in LaLiga in the 21st Century.
Only Atletico Madrid goalkeeper Jan Oblak (182) has reached the milestone in fewer games than Courtois (217).
However, the 29-year-old was more concerned with dropped points as Madrid missed the chance to increase its lead at the top of LaLiga to five points after city rival Atletico lost earlier in the day to Alaves.
"A clean sheet is not bad after conceding in the last games," he said.
"It is a bit of a bitter draw because it is at home and if a direct rival loses you want to win the three points. The point is not enough for us.
"We have prepared the game to try to put pressure on them, but in the first half they did very well. It was difficult to take the ball from them.
"We have missed too many passes. Sometimes it happens."
Madrid coach Carlo Ancelotti felt his tactics were spot on even though his side managed just two shots on target.
Both of them came in the second half after Madrid failed to register an attempt on goal in the opening 45 minutes for the first time under Ancelotti.
"I don't think the approach was wrong but correct," Ancelotti said.
"It was difficult to play between the lines because they defended very well. In the first half, we had difficulties because we did not have Etienne Capoue under control.
"In the second half we had more control, but we did not find a good opportunity. We put in more intensity, but it was very difficult to pressure them because they handled the ball well."
The match was the 800th that Ancelotti had presided over as a coach in Europe's top five leagues and notched up his 182th draw to go with 475 wins and 143 defeats.
Madrid is three points clear of second-placed Sevilla, which has a game in hand and beat Espanyol 2-0 earlier in the day.
"We finished with a clean sheet and that is positive after the last matches," the Italian added.
"Against Villarreal, if it's not your best night it's difficult to win. We are still up there in the league, and that is what matters."