Jordan Henderson (r.) und Jürgen Klopp
Image credit: Getty Images
The club sealed their 19th league crown with seven Premier League matches remaining after having won the Champions League, UEFA Super Cup and Club World Cup last year.
Henderson told British media the mentality of his team would never change.
"They'll want to keep going and keep improving because the hard bit now is continuing that consistency and intensity to keep going at the highest level, keep winning trophies," he said.
"That's going to be a new challenge for us to cope with and I've got every confidence from us that we'll meet it."
Henderson said manager Jurgen Klopp would help them maintain their focus.
"We see the manager as being someone who would never let distractions get in the way of what we're trying to achieve," Henderson added.
"After the Champions League (final) you could have asked would they still have that drive, that hunger to go on and win more? And I think we have proven this season we do."
Liverpool visit second-placed Manchester City in the league on Thursday. (Reporting by Shrivathsa Sridhar in Bengaluru; Editing by Peter Rutherford )