Coutinho, 25, finally completed a move from the Reds last month, but had failed to find the back of the net in any of his first four appearances. Valencia came close to scoring in the first half but the game produced very few chances in the first 45 minutes.
That scoring run has played a key part in Barcelona establishing a commanding nine-point lead in the Spanish league, and making the final of the Copa del Rey. "Today I got it and it helped the team get through to the final".
The scoreline saw the away side go one better than the result of the first leg last week where Luis Suarez's goal separated the sides at the Camp Nou.
In the final, on 21 April, Barcelona will face Sevilla.
"It'll be hard like all Finals, but it'll also be a great game and we have plenty of time to prepare for it".
However, despite the consistency with which they excel in the competition - they haven't lost a two-legged knockout game since 2013 - Valverde says reaching the final is still significant for the club.
"It's a very happy day", Coutinho told GOL after the match.
Nevertheless, Umtiti is suspended while Thomas Vermaelen has been out of action since picking up a hamstring injury in the 5-0 win over Real Betis on 21 January and is still uncertain whether the Belgium global could be back to face Getafe.
"It was very important to win the game and it'd be incredible to win four consecutive Copas, but that will only happen if we win".
Rodrigo Moreno came closest to scoring for the hosts when he crashed a header against the bar in the 13th minute and the Spain worldwide was thwarted again later in the half by Barca goalkeeper Jasper Cillessen.
Ernesto Valverde made one change to the team that played the first-leg as Andre Gomes replaced Aleix Vidal on the right flank.
Suarez did his part to make it 2-0 with eight minutes remaining when he pressured Valencia defender Gabriel Paulista and intercepted his pass.
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