Suarez scored a hat trick to lead Barcelona to a 5-1 demolition on Sunday. It was a stinging loss for Madrid that will heighten the pressure on the already beleaguered Lopetegui, who is only a few months into his job.
Local media reported Lopetegui’s dismissal was imminent, with former Chelsea and Italy coach Antonio Conte the leading candidate to replace him.
Madrid has now gone five rounds without a win in a stretch that includes four losses.
Wrapped in a winter coat, an injured Messi celebrated with the rest of the packed Camp Nou as Madrid endured its most humbling loss since a 5-0 defeat at Barcelona in 2010.
Suarez provided the goals and Barcelona coach Ernesto Valverde made the moves that proved critical in crushing a short-lived comeback by the visitors.
“We are very proud to have the best player in the world (Messi) on our team,” Suarez said, but “we showed that we are a great team and that we have a great coach.”
The win lifted Barcelona to the top of the Spanish league with 21 points, while Madrid was left languishing in ninth with 14 from four wins, two draws and four losses.
Lopetegui said he could turn Madrid’s season around.
“We all know how football works and the one who is ultimately responsible is the coach, but there is more to it and we all win and lose together,” Lopetegui said. “It’s early in the season and even though today is a sad day Madrid can have a good year. I still have strength to lead the group.”
The match was the first “clasico” since 2007 to be played without both Messi, who broke his arm last weekend, and former Madrid forward Cristiano Ronaldo.
But other than the first 30 minutes of the second half, Barcelona dominated its fierce rival — and European champion — even without Messi.
“Since last week when he was injured everyone was asking how we would cope, and the answer is the one that the team gave today,” Valverde said. “But the sooner he recovers, the better, because we miss him.”
Lopetegui, meanwhile, has been unable to restructure an attack that had been built around Ronaldo, who left this summer for Juventus.
Left back Jordi Alba was a pest to Madrid from the start. A long ball from Ivan Rakitic left Alba alone after fine control to romp into the area and pick out Philippe Coutinho, who provided a cool finish in the 11th minute.
Barcelona made it 2-0 in the 30th with help from a video replay after Raphael Varane barged into Suarez at the edge of the six-yard box.
The referee awarded the spot kick after consulting the video monitor on the sideline, allowing Suarez to step up and convert from the spot.
The match briefly swung the other way after the restart.
Lopetegui replaced Varane with Lucas Vazquez at halftime, and the forward played a role in Marcelo pulling one back in the 51st.
Seeing his team struggle, Valverde sent on defender Nelson Semedo and shifted Sergi Roberto into attack.
Suarez soon volleyed a headed pass from Roberto off the upright. He then linked up again with Roberto twice more to turn what was appearing to be an evenly fought contest into an easy win.
Arturo Vidal headed in a fifth goal from a pass by fellow substitute Ousmane Dembele with Madrid in disarray.
Madrid not only trails Barcelona, Atletico Madrid and Sevilla, but also Espanyol, Valladolid, Levante and Getafe.
“We can’t blame the coach. Every single one of us is playing very poorly,” Madrid midfielder Casemiro said. “But that is how our season has gone. It is a disaster.”