Henderson believes the positives from their last two games - even if one victory still resulted in their elimination from Europe on away goals - means they will not give up on the top four.
"We can take a lot out of the last two games," he told liverpoolfc.com.
"They were good performances and good results. Unfortunately we didn't end up qualifying for the next round of the Europa League but we gave it our best shot.
"We've got 11 games left and want to succeed in those games. We've done well of late - I think we've been playing some good stuff - we're still improving.
"[To qualify for the Champions League] would be a massive achievement.
"We'll give it our best shot. We know it will be difficult but we still believe we can do it.
"The coming games will be a good chance for us to showcase what we want to achieve."