Pellegrini's decision to introduce Deossa and Parrott at half-time proved decisive, with the pair combining for the goal that ended Real Madrid's perfect start to the season. The Chilean, who kept faith with his double pivot throughout, was delighted with how his substitutes changed the game.
"I'm very happy for Troy Parrott. Arriving at the club, a different kind of football... he'd had a few minutes in previous games, he had the chance that might have changed the result at Levante and missed it, and today he has not luck but the instinct to score that goal after Nelson Deossa's header, who I'm also very happy for — a player who gets questioned a lot," Pellegrini said.
"Starting a new stage at a new club, in different football, scoring the goal that beats Real Madrid, I think will give him a lot of confidence.
"He's a player with a lot of commitment and power, and with Cucho I think they'll make a good partnership, both playing together and separately."
Pellegrini rejected the idea that Betis had set out simply to contain their opponents.
"I don't do the same analysis, because I think the team went out to win from the first minute against a Real Madrid side that is, of course, difficult," he said. "Generally in the first half we each had a spell — we also had a very clear chance, and they had some too.
"In the second half I think we even had more of the ball, more territory in their half. They had dangerous set-piece deliveries where Álvaro Valles made three very good saves, but in the end we scored and took the three points against a great rival, in a very contested match that could also have been a fair result if it had finished level. That happens a lot in football — we made the most of the chance we had, and they didn't."
For Mourinho, the defeat was hard to reconcile with his side's overall performance.
"The team has played a great match. Sometimes you lose and can't explain how," he said. "Very dominant, imperious at centre-back, a lot of attacking play. If it had finished in a draw, we'd have been frustrated."
He was reluctant to blame the officials for the result, despite a controversial disallowed goal and a penalty save that went unreviewed for encroachment.
"I haven't seen it in detail, I can't comment," he said, before adding of his own booking: "I don't know why I got a yellow card. I accept it. I stood up because a Betis player looked like he'd died in front of the bench. I've seen a lot of people frustrated with the incidents, but I didn't see them myself. The referee let the game flow, and that's something I like."
Mourinho also praised the character of his squad despite the setback.
"I have nothing to reproach any of my players for, individually," he said. "When someone goes to take a penalty, we all go up together. Cucurella has cramp."