Henderson was told by Liverpool that he could look for a new club during the summer, and was heavily linked with a move to Fulham, but the midfielder has enjoyed a rejuvenation in his form during recent months.
After scoring goals in his last two Premier League games, Henderson believes that he is on the road to redemption at Anfield, admitting that the criticism was hard to bear at times.
"I wasn't playing regularly back in August so they gave me the option to go," Henderson told the Daily Mail.
"It wasn't a nice thing to hear. But I just had to take it on the chin. So I said no. I didn't want to go anywhere. I came to Liverpool wanting to stay here for the rest of my career. I certainly didn't want to leave after a year.
"I think I might have needed it, to be honest. I just feel if I keep working hard, and pushing on, I might not get as much criticism in the future.
"You have to go in and straight away try to match their ability. You need to learn to perform like they perform and that is a hard thing to do immediately. It's a step up and a challenge and for a good while I couldn't really do it.
"But this season the gaffer told me what he wanted from me, what I needed to improve, and I took it on board. He said I had to be better tactically, for example. He's been brilliant, to be fair, the advice he's given me."
Henderson has five England caps since making his debut against France in November 2010.