The Reds ended the last campaign on a relative high by finishing fourth in the Premier League for just the second time in eight years, meaning a place in the qualifying stage of the Champions League.
Any hopes Liverpool had of adding silverware to their collection came to an end during a dismal start to 2017, exiting both domestic cup competitions and fading well out of the title picture in a short space of time.
Henderson is hopeful that lessons have been learned from last term, however, challenging his teammates to pick themselves up and build on their fourth-place finish over the next 10 months or so.
"We have to set it very high with the squad, the players we have got and the manager we have got. We want to be winning things," he is quoted as saying by The Guardian. "That is the aim. We will go into every game and every tournament we are in wanting to win.
"We have to set the bar very high. There is plenty of competition for places. We have a fantastic group of players who want a better season this year and we will be working as hard as we can to impress the manager to get into the team. We always want to improve as a team.
"We have brought a couple of players in and have a couple of players coming back from injury. Everyone wants to improve and I think we have a young squad, getting better and learning. Last year put us in good stead moving forward and hopefully we will have a better season."
Henderson has featured in both of Liverpool's pre-season friendly matches so far, having missed the final few months of 2016-17 with a foot injury.