Luis Suarez produced a superb performance for Barca as he set up both goals in Thursday's win.
Coutinho, who joined Barca from Liverpool for a club record 142 million pounds ($197.66 million) in January, had been on the pitch less than three minutes when he scored, while Ivan Rakitic stretched the visitors' lead eight minutes from time. For me, it will be my first final [with Barca] and it's an important moment.
Barcelona will now face one of either Sevilla or Leganes in the final. 'I was looking for the goal in the first few games and today I got it and, most importantly, helped the team reach the final'.
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Valencia have not reached the final for 10 years, with Ronald Koeman leading them to the trophy in 2008 after knocking Barca out in the last four.
The Brazilian global made his Barcelona debut against Espanyol last month in a 2-0 win at Camp Nou.
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.
Trailing 1-0 from the first leg after Luis Suarez's strike separated the teams at the Camp Nou last week, Valencia nearly levelled the tie on aggregate early on.
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Valencia looked sharp on the counter-attack and seemed the more likely to break the deadlock, with Cillessen again called into action to deny Rodrigo.
Barcelona changed things at the interval by bringing on Coutinho for Andre Gomes, and the Brazilian made a near-instant impact as he got his right leg to Suarez's cross from the left to send the ball across Domenech and in.
The defender was seen grimacing and holding the injured knee at times during the match and was eventually substituted, allowing Colombian Yerry Mina to come on for his debut.
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