Still depleted by a spate of injuries and stifled by a downpour and a soaking pitch, Madrid rarely got going and had few goalscoring opportunities, while Betis kept them on their toes but also failed to carve out clear-cut opportunities.
A second goalless draw in three league games, after last Saturday's stalemate at struggling Getafe, left Madrid second in the standings with 71 points.
One positive note for Real was the return of record signing Eden Hazard after more than a month out injured and the Belgian looked sharp in the 15 minutes he played after coming off the bench, giving him a chance of a reunion with former club Chelsea in Tuesday's Champions League semi-final first leg.
"We didn't play well enough to get the victory and have taken a step back in the title race," said Real defender Dani Carvajal.
"We could have showed more hunger in the final third of the pitch and we've only got one point, which leaves us further away from the leaders. We couldn't get to the right crosses or anticipate where to run in the final few metres; we didn't get the small details right.
"We still want to send an optimistic message to the fans and we'll fight for the 15 points left but today was a chance to put the pressure on and we didn't take it."