The 25-year-old Brazil international was Barcelona's key transfer target but Liverpool rejected multiple bids from the La Liga side, saying the player was not for sale.
On Saturday, Coutinho made his first start of the Premier League season but failed help his side avoid a 1-1 draw against Burnley.
He discussed his "complicated month" for the first time in an interview with ESPN Brazil.
"What happened was a job offer and, in life, sometimes you get interested; sometimes you don't and, in my case, everyone knows that I got interested, my family too," said Coutinho. "It's an honour to receive an offer like that, but it's also an honour to be here (at Liverpool).
He continued: "I earned my place during the last four, five years and I've never had a problem with anyone here. I've always respected the support very much of the groups. The players, the directors, the technical staff. And that hasn't changed at all."
When asked whether a later date was agreed for a move to Nou Camp, Coutinho replied: "No, nothing that I know of. I'm in a place where I'm very respected by everyone and I also always respect everyone. No. It's all done now. I'm focused on working hard and to have a good year if possible. In the end, I have to help my team."
Coutinho played 78 minutes against Burnley before he was substituted, with manager Juergen Klopp confirming the player was suffering from cramps.
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