The 21-year-old Brazil international suffered a shoulder injury during the Reds' clash against Swansea on September 16 and had to undergo surgery to fix it.
Coutinho made his comeback for Liverpool during their 2-0 away defeat to Arsenal in the Premier League last weekend and could start against Fulham on Saturday.
"The fans' support was very important," he told Liverpool's official website.
"They were always sending me messages through Twitter, which were very gratifying. I read them every day and they motivated my recovery.
"I'm very happy to be back. I had six very difficult weeks and thank God I've made my comeback, but on the other hand I was sad due to the result [at Arsenal].
"However, that's over now and we must concentrate on our upcoming matches."