The Brazil star's imminent switch to Camp Nou was announced on Saturday, the 25-year-old agreeing a five-and-a-half-year deal and moving for a reported fee of €160 million, while his Barcelona release clause has been set at €400 million, goal.com reported.
Coutinho had long been a target for the La Liga giant, which was rebuffed several times in its attempts to sign him back in July and August.
Having handed in a transfer request, the attacker was always on borrowed time at Anfield and Klopp was disappointed to see him finally leave. However the manager saw no choice over the matter as Coutinho told him, the club's owners and even his own teammates that he wished to depart.
"It is with great reluctance that we – as a team and club – prepare to say farewell to a good friend, a wonderful person and a fantastic player in Philippe Coutinho," he told the Liverpool's official website.
"It is no secret that Philippe has wanted this move to happen since July, when Barcelona first made their interest known.
"Philippe was insistent with me, the owners and even his teammates this was a move he was desperate to make happen.
"Despite that, we managed to keep the player here beyond the summer window, hoping that we would be able to persuade him to stay and be part of what we are looking to do.
"I can tell the Liverpool supporters that we, as a club, have done everything within our means to convince Philippe that remaining part of LFC was as attractive as moving to Spain, but he is 100 percent certain his future – and that of his family – belongs at Barcelona.
"It is his dream and I am now convinced there is nothing left at our disposal to change his mind."
Coutinho moved to Merseyside in 2013 and went on to make 152 Premier League appearances, netting 41 goals, with Klopp lauding his input.
"Philippe has made a fantastic contribution to this club over his five years of service and as disappointed as we are he doesn't want to extend that, the relationship we have for him means with a heavy heart we wish him well," added the German.
"The player remained dedicated and committed to helping us win matches, producing good performances and training hard each day at Melwood after the summer window had closed, despite failing to convince us to allow him to leave during that period and that level of professionalism reflects positively on him."
Coutinho will link up with his new teammates in the coming days and watched from the stands against Levante on Sunday.
The 25-year-old is likely to be involved against Celta Vigo in the Copa del Rey on Wednesday.
And speaking before the deal had been announced, Valverde talked about his soon-to-be new addition.
"Coutinho is a great player, like many other players, and what I always like to do is value the players I have," he told reporters.
"There is speculation about great players around the world but we have many great players and I like to focus on mine.”
After selling Neymar in the summer, Barcelona brought in French youngster Ousmane Dembele for €105 million (£93 million).
The winger suffered a hamstring injury on his debut for the club back in August.