The long-running saga came to an end earlier this week as the two sides finally agreed on a big-money deal, worth £106m upfront and a further £36m in realistic add-ons.
Klopp tried his best to keep Coutinho at Anfield, having rejected three bids during the summer, but the German claims that it was too tough to deny the playmaker his "dream" move.
Speaking to reporters on Friday afternoon, Klopp also stressed that Liverpool will not rush to bring in any direct replacements.
"There was no other option. If there is somebody maybe who should be angry, massively disappointed, in this case, then it could be the manager of the club the player is leaving," he said.
"But I am not [angry], because I know we tried absolutely everything to convince Phil to stay here and carry on going together with us. It was his dream [to move to Barca] and it is the truth when I say he left Liverpool for only one club and we really had to accept that.
"The club was fighting until the last second and tried everything. It would have been very difficult if we had said, which we could have done, 'look, here is your contract and you have to stay here', and to use him in the second half of the season.
"We don't have to replace him. What we have to do is we have to step up. We played fantastic football without Phil. I don't want to sound disrespectful because I really liked him but we only have to carry on. We had fantastic games with him and not that good games with him. We have open eyes through this transfer window but we will not make crazy things. We want 'right' before 'expensive'."