Enrique's team put their relegation-threatened opponents to the sword, recording a 4-1 rout at the Estadio de Balaidos.
The win came courtesy of four goals in an 11th-minute period on either side of half time, including Nolito's brace, Charles' first-half effort and Stefan Mitrovic's own goal.
"This was a complete night for Celta fans, for the team and the club," Enrique told reporters post-game after watching his team move 10 points clear of the relegation zone.
"We knew the difficulty of our opponents, most of all for their need for points, but the game has turned out as we'd hoped.
"We were effective, supportive and we've played very good football. We were far superior to Real Valladolid."
Celta are virtually assured of top-flight football next season, though that will not be confirmed until Valladolid play their game in hand, which is against high-flying Real Madrid.
Regardless, Monday's result extended Celta's unbeaten streak to three games, something that did not seem possible after just two wins from six matches between November and December last year.
"It's been a difficult season for us and it seems like nobody remembers how much we suffered in November and December," he added.
"This is a day to congratulate everyone in the team for their faith, ability to remain enthusiastic and their hard work throughout the whole season.
"There's no sense in stopping that now though."
Meanwhile, Valladolid coach Juan Ignacio Martinez was lost for words after his struggling team slumped to their 13th game without a win away from home.
Valladolid are three points from safety, though they have played a game less than 17th-placed Getafe.
"I have no kind of excuse to explain what happened. This is not the way we've talked about in the locker room," he said.
Martinez added: "We've been good in the beginning but the game does not last 20 or 25 minutes.
"The third goal was the last straw, it was not worthy of professionals. We've lost a very important battle and now we are left with no margin for error."
