Coutinho, 25, was desperate to leave Merseyside for Catalonia this summer and submitted a transfer request as he tried to push through a deal between the two clubs, but Liverpool stood firm and refused to grant the Brazil international's wish.
Evans, who won the League Cup during his four-year sting in charge of Liverpool, praised his former club for refusing to be bullied by Barcelona over Coutinho and is confident the former Inter Milan starlet will "fulfil his agreement" and perform for Klopp's men this season.
"He wanted to go but Liverpool said no," Evans told talkSPORT. "Liverpool said you're not going, we want you to stay. We've got a top player and we don't want to become a team that sells their best players – and they've stood their ground.
"Obviously, it was a massive offer and his head's been turned. And who wouldn't want to go to Barcelona? But at the same time, you sign a contract at one club and sometimes you have to honour that contract.
"And to be fair to Coutinho, I'm hopeful that he'll give his best. He's that type of lad from what I've seen and he'll go out there and play his best football and try and do his best for Liverpool.
"You can't just have it your own way. You are contracted and sometimes you have to fulfil that [agreement]."
Liverpool's refusal to allow him to move to Barcelona may be a bitter pill to swallow for Coutinho, who has looked in fine fettle for Brazil this week despite apparently suffering from back problems, but Evans believes the talented attacker will remain committed to the Reds and play as best he can in order to secure his place in the Selecao's line-up for the World Cup in Russia and keep his Barcelona dream alive.
"At the end of the day the World Cup is coming up and he has to get in the Brazil team," Evans said.
"Hopefully he has an honest style about him and will think: 'Ok, I'll accept the decision that Liverpool don't want to sell me and I'll play my best'. When the time comes he might get his chance in six months or a year's time to move to Barcelona.
"I'm sure we've improved him in many ways since he's come to Liverpool and he's become one of our top players."