The 26-year-old has gradually begun to show the qualities that convinced Betis to bring him to the club, while Pellegrini's demands have played an important role in his progress.
Riquelme revealed that a conversation with the Betis manager proved to be a turning point in his time at the club.
"I had a conversation with him that changed my mindset. The truth is that I was very grateful to him. He insisted and said: 'A player with your talent and your abilities has to do it,'" Riquelme told ElDesmarque.
"From then on, I said to him: 'Look, boss, I'm going to work on that, I'm going to do it.' And I've been taking steps forward."
The Spain international explained that Pellegrini continued to reinforce the message, making it clear that he expected more from Riquelme because of the range of qualities he possesses.
"He kept telling me, he kept showing me that if I gave him this, he would give me something back," Riquelme said. "That conversation was a before and after in my time here."
Pellegrini's assessment of his player was based on the technical and physical attributes he already possessed.
"He told me: 'You have all the abilities in the world to do it. You're quick, you have one-on-ones, you combine well, you have a good pass, you shoot well,'" Riquelme said.
"If you didn't have three or four of these things, I wouldn't demand them from you, but because you have them all, I have to demand them from you."
Riquelme also revealed that he had opportunities to leave Betis during the summer but decided against a transfer.
"There were several offers, that's true, but I spoke very clearly with my brother, who is my agent, along with Fede, and I had absolutely no intention of leaving Betis," he said.
The midfielder said his feelings towards the club, combined with the end of the previous campaign and the prospect of Champions League football, convinced him to stay.
"I still have this enormous feeling of gratitude towards the club. Also, my feelings during the last two months of last season were very good," Riquelme said.
"So I said: 'Mate, it's time to fight.' On top of that, we had a very exciting project, which is the Champions League."
Riquelme made his decision clear to those around him.
"I'm a Champions League player and I said no, that I was staying, that I wanted to fight, that I was convinced about it and that I wanted to stay here until I die," he said.