Philippe Coutinho's first goal for the Catalan club and a signature Ivan Rakitic finish sealed the 3-0 on aggregate victory which will see them face Sevilla on April 21.
Speaking to the club website, Valverde said: "Our opponents and their whole city were very much up for this game. We dominated tonight although they did have their chances. But we deserved to qualify.”
"I would have preferred to have had the game sorted out earlier...if Valencia hadn’t hit the crossbar they would have been right back in the tie.”
Barca will be looking to earn their fourth Copa del Rey title in a row when they face Sevilla in what could be Valverde's first piece of major domestic silverware with the club.
The manager continued: "We’ve beaten some tough teams like Celta, Valencia and Espanyol in this competition, so I’m very happy. Barça have played in a lot of finals, but this is just my second. I hope I get more luck than I did in the last one."
“I already have the experience of playing one final at the opposition’s ground. I wouldn’t want to have to do that again."
However, they could seal the title by then if they continue in the same fashion, remaining unbeaten and currently nine points clear of second placed Atletico Madrid.
"What we intend to so now is focus on La Liga and the Champions League, where we have a very difficult game ahead," Ernesto said. "But next up it’s Getafe. My players have the mentality to do what the club demands.”