Álvaro García had put Rayo ahead inside four minutes at the Ramón Sánchez-Pizjuán, but Jon Guridi levelled from the spot early in the second half before Peque's stoppage-time penalty completed the comeback, even after Kike Salas saw red for Sevilla in the 88th minute.
"We've gradually overcome psychologically several things that happened to us in the match. First the goal, because it's our mistake, then the disallowed penalty and the red card. I think that shows the team has been very good. From my point of view we deserve the win," García Plaza said.
The coach felt his side grew into the contest after a difficult start.
"The team started well, it kept growing in the second half and in the end, with one fewer man, it was even able to come from behind. Plus, how the goal against us comes, which isn't a move from them, it's our error.
"It's the home debut and then there's a penalty incident that gets given and VAR overturns it and that hits you with another blow. We had a lot of shots on goal and I think we were very good in the second half."
García Plaza was quick to single out the player he felt deserved credit for winning the decisive penalty: "The penalty action for me is down to Manu Bueno, who made a spectacular play. Please name him too because he deserves it."
He also praised the impact of new signing Robbie Ure.
"Robbie (Ure) has been very good, he's given us everything we asked of him. Sometimes he doesn't know what Ejuke or Rubén are going to do when they get the ball, but he came on for 45 minutes and gave us a lot. I'm very happy with him. Robbie gives us a lot of work holding the ball up, competing for it, but he still has to give us more, he's trained for very few days."
Asked about his substitutions, the coach revealed he had even considered a bolder change before backing off given the numerical disadvantage.
"In modern football you can change half the team. At one point in the match I even thought about trying Robbie and Isaac together for a while, but with the card I was worried. The players on the bench are hugely important."
García Plaza also admitted he had approached referee Ricardo de Burgos Bengoetxea to acknowledge a mistake of his own.
"I recognised an error to him because I had appealed, before Kike's sending-off, for a handball that wasn't one."
He was effusive about the reception from the home support despite the club's modest recruitment this summer.
"Sevilla's fans aren't stupid, they know what there is. The atmosphere is brilliant. This isn't the Sevilla of big signings, and the fans know we're going to need them to the maximum. But we already have three more points and they taste very good because eight academy lads, as I say, played. I'll shut up now, because I could say something, but I'll shut up."
Guridi, who joined Sevilla this summer, described the emotion of scoring on his debut.
"We knew it was going to be very important. The club had gone five years without winning the first game and we were convinced we were going to manage it. It's true we started badly, conceding a very early goal, but the team reacted well, with personality. It didn't give up."
The Basque midfielder felt Sevilla's dominance after the break was clear even once Salas was sent off.
"In the first half we had our chances, we caused them a lot of problems with crosses from wide, and from the start of the second half we went out after them, you could see we could turn it around. You could see it even with one fewer man, that we weren't settling for the draw.
"I'm a person who keeps their feet on the ground, I don't like getting carried away when things go this way. It's a happy day for me because of the goal and because of the win, but we have to keep working because this has only just started. There's a lot of quality in the first division and you can see that from the first game."
Guridi revealed he had been first choice on the penalty list well before the moment arrived.
"I was first on the list for set pieces to take the penalty. I went with personality, with confidence. In the end, it's the ones who take them that miss them, and this time I scored it. Onwards with this momentum and this confidence."