The Reds enjoyed a stellar campaign last time round to become European champions and amass 97 points in the Premier League .
However that points total wasn’t enough to knock Man City off top spot as they defended the title by the finest of margins.
Now Klopp believes his squad must improve on their attempts of last season if they are to catch their Manchester rivals.
Speaking in his matchday programme column , Klopp said: “A new season is always about opportunity. I think this coming one presents the best kind of opportunity for all of us in the LFC fold.
“As the team, we know we have the opportunity to be better than we were last season. This I love about football.
“Regardless of what came before you know there are new challenges and new memories to make.
“This team, since I have been fortunate enough to lead them, has been all about progression collectively and individually.
“They know standing still means you actually fall backwards. The Premier League, the domestic cups and Europe – all our opponents will make strides forward.
“Our strides can and must be bigger if we want to achieve.”
The Reds have the chance to top the table from the off as they start their Premier League campaign in the opening fixture of the season against Norwich on Friday.
Klopp’s side are firm favourites to overcome the newly-promoted side at Anfield, but he insists his players must step up to the challenge week-in, week-out, if they are to better last season.
“I hear the words often, after a season like we just had, about how difficult or how important it is to ‘go again’. I don’t dislike the sentiment and there is merit to it, but simply ‘going again’ won’t be enough,” he added.
“We need to be even stronger, even fitter, smarter, more committed, greater focus.
“Maybe a slight change on the sentiment: ‘improve again’, maybe ‘progress again’.
“Here is what I know for certain: it will be the toughest, most challenging season we will all face, and that is because of the quality we compete with.
“Starting tonight we face outstanding players, led by brilliant managers and coaches week in and week out – it doesn’t stop.”
There is added pressure on the Merseyside club to end their wait for a Premier League title, but Klopp had one final note for the club’s fans.
“If I had one message for the coming season, to everyone who cares about this amazing club, it is that we are ready for some great times if we are prepared to work together to achieve it.
“We can stay together at all times if we want it this way, good times and bad.
“As the team, management and players, we know what our responsibilities are and we are hungry and eager to deliver more.
“We know our supporters will be the wind at our backs. The rest is about the journey and making sure you take all the joy you can from the moment.”
Liverpool’s match with Norwich kicks off at 8pm (GMT) on Friday August 8.