Gerard Moreno had given Villarreal a 29th-minute lead before Cucho Hernández levelled in the 39th minute and Natan turned the game around six minutes later, completing a first-half turnaround that took Betis to 12 points from their opening five matches.
"Overall it was a really good match," Pellegrini said. "I'm delighted because football is a spectacle, and I think these are two teams that know how to play and go looking for the opposition's goal. We put in a really complete performance; maybe we lacked a bit of composure in the four or five very clear chances we had in the second half to finish the game off.
"We didn't convert them, but we kept looking to attack with defensive security, so against a very good team in their own stadium, I was very pleased with what the team did."
The Chilean acknowledged the nervous moments that followed once Real Betis failed to extend their lead, but insisted his side controlled the game throughout.
"Of course, when you're only ahead by one goal and miss that many chances, football usually punishes you and the equaliser comes," Pellegrini said. "I think we were switched on defensively and kept looking for their goal, even if we were a little rushed and imprecise in the final third.
"It isn't easy to create that many chances against a team like Villarreal here at home. Overall I was very pleased, especially because we gave Villarreal no real chances to hurt us, particularly in the second half."
Pellegrini also pointed to the creative depth within his squad as a source of encouragement for the season ahead. "We have a lot of very creative players," he said. "It's not just those two, there's also Fidalgo, who plays very well, then Gio Lo Celso, Ceballos and Isco. We have creative players because this team tries to play creatively and always look for the opposition's goal."
For Villarreal, the defeat leaves them without a win in LaLiga or the Champions League this season and inside the relegation zone. Manager Iñigo Pérez took full responsibility afterwards.
"If I had an explanation, I'd fix it," Pérez said. "I'm not hitting the level we need. I'll keep insisting until it comes. I don't know if it's anxiety, fear or helplessness. We need to reflect seriously on the state we're in as a group and make decisions. I think it's a lack of ability from the coach. That's where I need to have an impact - to look at myself and see what I can do to change this."