Published: 2017-03-13 18:51:40 BdST
Real fell behind to an embarrassing own goal by goalkeeper Keylor Navas in the first half but turned things around with a diving header from top scorer Cristiano Ronaldo before the break and a late headed goal by captain Sergio Ramos from a corner.
Real top the standings on 62 points, two above Barcelona who suffered a shock 2-1 defeat at struggling Deportivo La Coruna four days after their epic 6-1 win over Paris St Germain at the Nou Camp took them into the Champions League quarter-finals.
Zidane's side also have a game in hand on Barca and third-placed Sevilla in their bid for a first Liga title since 2012.
"We didn't have it all our own way and that's normal, but I am happy. We must congratulate all the players because we had to be patient, the result was fair in the end even if it didn't all go our way for the whole game," Zidane told reporters.
"They (Betis) played most of the game in their own half, they defended well and caused us problems on the counter attack but we're happy with the result because it wasn't easy. The pressure was on us but it doesn't end here, there's still a lot to play for and we know that."
Betis were the third team in four games to take the lead against Real after Las Palmas and Napoli and on each occasion Zidane's side got back in the game with a goal from a set piece.
"I'd be more relaxed if we went two or three goals up at the start of every games, but this is just the way things go," the Frenchman said.
"We know that we're capable of scoring at any time. Today we showed patience when the going got tough and we kept our heads. We know that we're a threat from set pieces, but I'd like us to score more goals from open play."
Zidane also backed Navas after Real fans booed the keeper, who turned a soft shot from Antonio Sanabria into his own net and had been fortunate not to be sent off earlier in the match for upending Betis winger Darko Brasanac.
The Costa Rican compensated for his howler, however, with a vital save to prevent Sanabria from equalising in added time.
"Everyone makes mistakes, they're part of the game and everyone supported him in the dressing room at halftime," added Zidane.
"Keylor has a big personality and he made a great stop at the end. He made up for the mistake and made sure we got all three points."