"If somebody is a character and wants to celebrate position one in November then he will not play in December anymore because I see it pretty quick," Klopp told British media.
"But these things usually don't happen. The players are here in this situation because their character is really good. It is a long way to get here. It is not like they are surprised about success whether it is individual or as a team.
"This is success but if you then celebrate this and don't be professional anymore then you have a problem."
Klopp, however, said he has yet to see any sort of complacency from his squad this season.
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"It is not too difficult. Nothing has happened until now. It is better to be one time in first place than never in your life but it is not really important in this moment. There is nothing to think about," he added.
"If I went to the players and said 'Don't think we are first' or 'We are first but nothing has been reached' they would think I'm silly because they know this already. Stay cool, play football and see what happens."
Liverpool host second-bottom Sunderland at Anfield on Saturday.
(Reporting by Shravanth Vijayakumar in Bengaluru; Editing by John O'Brien)
