Coutinho, who Barcelona signed from Liverpool for £146m last season, endured a miserable evening and was withdrawn for Nélson Semedo after the hour mark.
The 26-year-old was whistled by the home supporters as he departed the pitch, amid speculation that Barcelona will attempt to offload him this summer.
But Messi, who scored two stunning goals to put Barcelona in complete control of the tie, rushed to the Brazilian’s defence after the full-time whistle and urged the home crowd to get behind him.
“This is a time when we have to be more united than ever, both as players and fans,” he said immediately after full-time.
“This is something we have to achieve together and it is not the moment to criticise anybody.
“It is ugly to see [the crowd] treat a team-mate like that.”
Barcelona are now the overwhelming favourites to progress to the Champions League final in Madrid next month, with the second leg against Liverpool to be played at Anfield next Tuesday.
Join our new commenting forum
Join thought-provoking conversations, follow other Independent readers and see their replies