Valencia's Eliaquim Mangala, who was later sent off, scored from Daniel Parejo's corner to give Valencia the lead after 29 minutes at Camp Nou.
But goals from Luis Suarez, Andre Gomes and a brace from Lionel Messi ensured Barca ran out 4-2 winners in the end, with Munir El Haddadi scoring Valencia's second.
Deportivo La Coruna scored two goals from corners to beat Barcelona 2-1 in the Blaugrana's previous game, but Luis Enrique is unconcerned by the trend.
He told Marca: "It is football. You enter into a dynamic.
"You can go one hundred corners without conceding, and then you concede three.
"Mangala's goal is entirely to his credit."
The result moved Barcelona back to within two points of La Liga leaders Real Madrid ahead of the international break, and Luis Enrique was satisfied with his side's performance despite their defensive frailties being exposed.
He said: "It was an entertaining game for all of us, with chances for both of us until the last minute.
"We played a good game. Valencia made us work hard, but we generated many chances and it could have been a better result.
"We got three points against a difficult opponent."
Luis Enrique singled out Gomes for praise after the 23-year-old scored his first goal for Barcelona since joining the club from Valencia in July 2016.
"I'm triply happy for him," said Enrique. "There's nothing better than your stadium applauding you.
"I am sure that Andre Gomes will be a very important player in the coming years in Barcelona."