The Merseyside outfit are 10 points away from a top-four position in the Premier League table with 11 games left to play.
"[We] want to succeed in those games," Henderson told the club's official website.
"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 Reds are preparing to go up against Wigan Athletic this Saturday.