Ezzalzouli's effort proved decisive, though José Bordalás felt his side had been on the wrong end of a refereeing decision.
Bordalás praised his players' effort, but singled out the goal as the turning point.
"The team goes away sad because we've lost. Congratulations to the lads, they made a huge effort, they competed within our means," he said. "There have been details that have penalised us, above all the goal, which is at the very least strange — Isco is in front of [goalkeeper David] Soria. He has no visibility, and the rule says that when the view is obstructed, it should be disallowed."
Bordalás also felt Abde may have used his arm in the buildup.
"Yes, it was tucked in, but he uses it to cushion the ball. Those actions are usually a handball, but beyond that, I'll take the effort of the team," he said, while accepting a red card shown to Mario was correct, if lacking malicious intent. "It's clear he pulls his leg away at the last moment. He's impetuous but without malice."
Manuel Pellegrini, whose side won for the second time in a week having also beaten the Ligue 1 leaders in the Champions League, was delighted with a start that has brought 15 points from a possible 18.
"It's not easy, and on top of that fitting in a Champions League away game against the leaders of the French league and winning it. I think it's a very motivating start, and a demanding one, as we keep trying to get as high as possible," he told DAZN.
Pellegrini praised a disciplined defensive display against a well-organised opponent.
"Getafe are a complicated team, they defend a lot and are very strong. Luckily we managed to convert that goal. We had three or four fairly clear chances," he said. "The team was very good defensively — they practically didn't reach our goal."
The Real Betis coach also hailed the impact of Abde, back from a long injury lay-off, and Dani Ceballos's return from Real Madrid.
"It's a lot of time, practically four months in which he couldn't play with continuity, that's why we're limiting him to a maximum of 70 minutes," Pellegrini said of Abde. Of Ceballos, he added: "He's a very important player who spent no less than eight years at a club like Real Madrid... he waited for Betis until the end because he wanted to come home, so he's making a very important contribution for us."