On a day when second-placed Atletico Madrid were held to a 1-1 draw by Sevilla and Real Madrid suffered a 2-0 home defeat against Real Sociedad, Barcelona edged a tight game at Coliseum Alfonso Perez to open up a gap on their rivals.
Memorable first-half goals from Lionel Messi and Luis Suarez put Barcelona in charge before Jaime Mata scored in a brave Getafe fightback, but the champions proved too strong for Pepe Bordalas' side.
Valverde's future at Camp Nou had been the subject of speculation in the week leading up to the game and, having delivered a result that leaves his position and the Blaugrana's title defence looking all the more secure, he issued words of caution.
"It has been a hard match," Valverde told reporters. "We knew it would be as well.
"We withstood the challenge and picked up more points than those behind us.
"For us it was crucial to be focused. Getafe is a strong rival and pressured us a lot. We have to recognise that they had chances too."
One very good reason to go to sleep happy tonight pic.twitter.com/S7yJlfDd0f— FC Barcelona (@FCBarcelona) January 6, 2019
Getafe are seventh in the table, just five points behind fifth-placed Real Madrid, whose chances of pushing Barcelona for the title appear to be fading.
Valverde underlined Getafe's quality while indicating that he felt the title race remains open.
"Getafe is an uncomfortable rival for Barca and for anyone," he said. "They are experts in winning second balls. They are a hard and difficult team, as the table reflects.
"I don't think too much on the rest of the results. I think about what we have in front of us and never rule out the teams in Madrid or the rest."
Valverde's opposite number Bordalas lamented the decisions that went against his side, who had a goal ruled out in the ninth minute.
Getafe could have been playing against 10 men after Arthur appeared to connect an elbow with Angel Rodriguez's face but the Barcelona midfielder escaped with only a booking.
Mata also missed a glorious opportunity to equalise after rounding Barca goalkeeper Marc-Andre ter Stegen, and Bordalas said: "The feeling is bittersweet.
"We have had occasions: one goal annulled, a possible red card. We feel very much harmed.
"We made a great match. It is true that they have Messi, the best player in the world, but all in all I think that we have been able to play in the match.
"We had clear chances that we could not take."