The Reds dominated the game against the Gunners, hitting the post twice and missing a penalty, only to see Robin van Persie's two goals from two shots clinch a 2-1 win for the visitors.
The England international had one of his best games for Kenny Dalglish’s side after struggling in the League Cup final two weeks ago and feels his team-mates can bounce back starting on Saturday against his old club Sunderland.
He told reporters: "I don't think it is over. There is plenty of football left. We've just got to keep working hard, try to get the right results and keep playing like we did against Arsenal.
"Obviously we're disappointed with the result because I thought we should have gotten something out of the game.
"We played some good football, particularly in the first half, and had some good chances but that's the way football goes.
"We've got a big game next week [at Sunderland] and we've got to try to bounce back."
Henderson also believes that the amount of chances the Merseyside outfit create give them hope of re-igniting their Champions League chase at the Stadium of Light.
He told the club’s official website: "If we keep playing like that, I am sure we'll get better results.
"I think we can take positives from the performance. Everyone was disappointed after the game, but I think over the next couple of days we'll realise we did play some good stuff and created chances - that's all you can ask for.
"We'll keep working hard and hopefully next week will be a better result."
How do you stay up to date with football when on the move? With http://m.goal.com – your best source for mobile coverage of the beautiful game.