The 28-year-old set up Jamie Vardy for England's second goal in a 2-0 World Cup qualifying win over Lithuania on Sunday, having also started against Germany in a friendly on Wednesday.
Klopp expressed his frustration after Adam Lallana sustained a thigh injury while playing for England this month, but refused to fault manager Gareth Southgate for selecting the midfielder.
Jurgen Klopp's preparation for the derby has already been disrupted by the continued absences of Jordan Henderson and Daniel Sturridge.
'I really think we could handle these situations better if we work together.
Fenway Sports Group, Liverpool's owners, have hired a private jet to get Firmino and Philippe Coutinho back in time so they can train today but it is a far from ideal situation.
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Although both will be worn out after their worldwide exploits with Brazil, they're both set to start against Everton and will of course play a key role in upcoming games. 'Somebody said I was relaxed about it, I could not be less relaxed about this - but it is not about blaming Southgate.
The German tactician will be unable to call upon Adam Lallana who suffered an injury during global duty with England.
Ragnar Klavan has been battling the defender for a starting spot and with Lovren now back fit, Klopp must decide who will start the Merseyside derby against Everton on Saturday (12.30pm).
Lallana's worth has also become evident on the worldwide stage as he scored on three successive England appearances earlier in the campaign.
Exclusive stats from Oulala.com show just how influential Henderson has been for Liverpool this season, along with the numbers behind their dip in form when he has not featured. His creativity has made him crucial in linking Liverpool's midfield and attack, and has translated into a lot of chances created and goals scored.
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