Coutinho has endured a difficult season at Barca, but displayed his quality with an exceptional long-range strike that put Valverde's side 3-0 up against United in their Champions League quarter-final second leg.
The Brazil international risked the wrath of Barca's fans with his celebration, however, holding his fingers in his ears in a seeming an act of defiance against his critics.
That celebration has led to plenty of criticism, including from former Barca star Rivaldo.
And while Valverde insisted that Coutinho must accept criticism is part of playing for Barca, he is disappointed that the celebration has overshadowed a sublime goal and fine individual performance.
"In regard to criticism, we are in the world of football and subject to continuous criticism. And you always have to face [the critics]. Coutinho is the same as everyone.
"I have not talked with him. He made a gesture. What surprises me is that they talk more about the gesture than the goal.
"I did not find anything special and I did not think it was disrespectful to anyone. We give a lot of hype to anecdotal things.
"Coutinho has had a year in which he has suffered criticism, but the important thing is that he played a match that I am happy with."
Barca hold a nine-point lead at the top of the table with six games remaining, but Valverde shrugged off the suggestion complacency could set in as they hunt down a La Liga, Champions League and Copa del Rey treble.
"It's been a good season but we want it to be better," Valverde said.
"We are first in the league. We are going to play a final against Valencia and then we will see if we are in the Champions League final.
"We are where we want to be. There have been two times in our history that Barca have won the treble.
"Right now, what drives us is our need to win. There are nine points on the table this week, which is just what we need to clinch the championship."