Coutinho broke the deadlock after latching onto a superb cross from Luis Suarez to steer the ball inside the far post and into the back of the net.
The Brazilian will be delighted to register his first goal for the club after a number of chances in his first four games.
He told Valencia's official website: "We are expecting a long game, a very tough game, and hopefully after the 90 minutes we will be able to say that we are in a Copa del Rey final".
They were condemned to a sixth straight defeat in all competitions as Suarez pounced on a Gabriel Paulista error and set up Rakitic to make it 2-0 on the night.
"It's a special thing to reach a final and I am sure it will be a great game, but also a hard one, like all finals are".
Barcelona have lifted the trophy for the last three years and face Sevilla in the final on April 21, a re-run of the 2016 showpiece which the Catalans won 2-0 after extra time.
"More importantly, though, it was able to help the team reach the final".
Rodrigo Moreno came closest to scoring for the hosts when he crashed a header against the bar in the 13th minute and the Spain global was thwarted again later in the half by Barca goalkeeper Jasper Cillessen.
But Cillessen proved his worth this evening with a stunning stop to deny Jose Gaya, palming away his volley.
Coutinho was perhaps surprisingly left out of the starting line-up in favour of Andre Gomes at Mestalla as head coach Ernesto Valverde named a strong side that included Gerard Pique, who recovered in time from a knee problem.
The only concern for Barca will be the sight of Pique in obvious discomfort after going off late on to be replaced by €11.8m man Yerry Mina, who made his debut.