In a series of Twitter posts, the Norwegian questioned the timing of the forward's decision - which came on the eve of the team's Premier League opener at Watford - but called on supporters to "respect that players have different dreams".
"Coutinho has asked to leave Liverpool. What now FSG? Klopp? Not what we needed before the first game," Riise wrote.
"Tough situation for the club and player. We want to keep him as he is brilliant! He wants to leave as Barca is a dream for him. Not easy.
"We all know Coutinho loves Liverpool. Always will. No reason to hate him. Respect that players have different dreams. Needs sorting out ASAP.
"The timing of this transfer request is bad though! So many ways he could have played this better. For the club, teammates and fans."
Coutinho, recently the subject of a rejected Barcelona bid, is believed to have emailed his transfer request directly to the club, rather than go through the usual channel of his representatives.
The Brazilian was not included in the squad for Liverpool's clash with Watford, said to have been omitted through injury.