Los Blancos were in need of a response, having been jeered off by their own fans following the midweek 3-0 Champions League defeat by Spartak Moscow.
Karim Benzema’s early strike, the France forward later going off with an ankle problem, was enough to secure victory which put Real Madrid third in the table and closed the gap on Atletico Madrid and Barcelona to two points.
Relegation-battlers Rayo, though, could have snatched a dramatic equaliser in stoppage time when Thibaut Courtois was forced into a superb double save.
Nevertheless, Real can now head off to the Club World Cup campaign in the UAE in positive mood as they prepare for Wednesday’s semi-final against Japanese side Kashima Antlers.
“I’m satisfied, we put in a very good first-half performance. We dominated the ball, made the most of the space, created chances and pressed very well,” Solari said.
“We should have gone in with a bigger lead at the break, but that’s football, when you’re not clinical you know you’ll have to dig in at some point.”
Solari added at a press conference: “The pace dropped in the second half, but we didn’t give them a sniff until the final minute and Courtois did brilliantly.
“When you don’t kill the game off, these things will happen. I’d be more concerned if we weren’t creating the chances.”
Solari confirmed both Benzema and Marco Asensio, who picked up a thigh problem, would be assessed on the trip to Abu Dhabi.
“We’ll have to see, we haven’t had a chance to have a look,” the Real Madrid coach said.
Isco was an unused substitute, left warming the bench, but Solari played down suggestions of a rift with the midfielder.
“What I’m interested in is that all of the players are happy and committed. That’s what we all work towards, so that they’re all available,” the Real Madrid coach said.
“I try to get things right when I name my squads, line-ups and with my substitutions. I’m sure I make mistakes, but it’s all part of my job.”
Solari was happy to send the home fans, who will not see another match at the Bernabeu until January, happy heading into the Christmas break.
“I loved the way the supporters got behind us right throughout the whole game, we’re delighted with them. We wanted their backing and they backed us from start to finish and we gave them reason to with our play,” he said.
“It’s normal that there was that vibe after the chance that Rayo had right at the death.
“We’re happy to have topped our Champions League group, progressed in the Copa de Rey and to have cut the lead at the top of LaLiga.”
Rayo coach Michel felt his side could have taken something from the match.
He said: “In the second half, with the change of system, we were more comfortable.
“I’m satisfied, but we have a lot of room for improvement, although the performance of the team is there.”
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