García and academy product Pedrosa struck inside the opening 20 minutes to put Rayo firmly in control, with Roberto Fernández's second-half reply proving no more than a consolation for Espanyol. The result gave Rayo their second win of the season, coming just days after a demanding fixture against Real Madrid.
"The first half was stellar, we were dominant from start to finish, we created a lot," Beñat said. "We could have gone in at half-time four goals up. In the second half we needed to finish it off, they brought on some starters and we weren't at the level of the first half - that's logical in football.
"We had two or three chances in the second half we should have scored. In professional football you're always going to suffer at some point. It was an extraordinary match in the first half and a hard-fought one in the second."
Beñat reserved special praise for Álvaro García, who scored the opener and set up the second.
"He's one of the best wingers in LaLiga, of vital importance. He's a gentleman and tactically a phenomenon. You need to tell him very little for him to understand everything," Beñat said. "He represents personally and footballistically what Rayo Vallecano is about. He's one of our captains and I'm delighted with him."
The Basque coach also addressed the club's ongoing situation playing home matches away from Vallecas, at Leganés's Butarque stadium.
"It's a very good, very important record. We play at home, but not in our own home, and that's a huge handicap for us and a bonus for the opponent," Beñat said. "They've treated us very well in Leganés and we have to be grateful for that."
For Espanyol, head coach Manolo González was scathing in his assessment of a first-half collapse that undid his side's chances.
"We were all bad, the eleven of us, not just three," González said. "There isn't a single player from that first half we can salvage, not one. We touched three players from the XI the other day, because Edu had knocks and we obviously had a game on Friday. We thought Rafa and Gabi would find the opponent's rhythm - that didn't happen, and from there we were chasing the game."
González explained the turnaround came from correcting a tactical error rather than personnel changes.
"At half-time we adjusted what we'd already prepared, matching their three-man midfield zone, which we hadn't done in the first half because they played alone and we didn't press," he said. "When you do everything wrong, of course the second half looks like you did everything right."