The 21-year-old spent three seasons at Inter, with his arrival in Milan coinciding with their fall from grace after five consecutive Serie A titles and a Champions League crown.
Coutinho said it did not work out for him at Inter after the arrival of Rafael Benitez, but their squad depth made it tough for him to get consistent minutes.
"Jose Mourinho was the manager when I was preparing to join them, but he left before I moved to Italy," the Brazilian told the Daily Telegraph.
"It was a difficult period, strangely, because they had won the national championship five times and just won the Champions League but the club was preparing for change.
"Rafa Benitez had just become the manager and he was prepared to give me opportunities straight away as a younger player, but there were good players there who won a lot at the club – really good players – and things were not settled and it turned out not so good.
"I had a good relationship with Rafa, he was always very considerate towards me and gave me a lot of confidence. He cared a lot about all the younger players at Inter."
Coutinho said he 'didn't think twice' about a switch to Anfield when the opportunity presented, and he has flourished with the Reds - making 12 starts in his initial season in 2012-13, before making five starts and a sub appearance this Premier League campaign.
"Sometimes you can be a good player at a good club and for some reason it just does not work out," he said.
"There is no explanation for it. Then you move to another club and it fits perfectly straight away and you feel comfortable.
"I had some chances at Inter, but after a few years – certainly by the time Liverpool were interested – I was not getting many chances.
"As a footballer all you ever want is the chance to play, and show people how well you can play. I knew at Liverpool I would get that opportunity so I didn't think twice.
"You look at a club and you see a top European team, with top players and top ambitions to win every major trophy, even if it will take time. I didn't even have to think about the decision."
