Liverpool were held to a 1-1 draw by Manchester City on Sunday.
The Reds got off to a quick start, with Mohamed Salah firing home a penalty after Kyle Walker brought down Sadio Mane inside the box.
City levelled through Gabriel Jesus, with the Brazilian striker poking home after turning Trent Alexander-Arnold inside the box.
The hosts had another golden chance before half-time after Joe Gomez blocked a Kevin de Bruyne cross with his arm.
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But the Belgian midfielder stepped up and rolled his penalty wide of the post, and the two sides went into the interval level.
After a blisteringly fast-paced first-half, both teams appeared much more fatigued in the second period.
Both sets of players appeared significantly tired, and neither were able to reach the same energy levels as they showed in the opening spell.
And after the game, Klopp appeared to blame the pile-up of fixtures for his side’s lack of spark and pace.
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He echoed Solskjaer’s comments about fixture scheduling and confirmed he had spoken with the Premier League.
United played Istanbul Basaksehir in the Champions League on Wednesday night, before being asked to face Everton in the midday fixture on Saturday.
And the Liverpool boss was heavily critical of that decision from the Premier League, claiming the powers that be will need to look at the schedule and make some changes.
Klopp told BBC Sport: “I have spoken to the Premier League. No team on a Wednesday night should have the 12:30 kick-off on Saturday.
Speaking to Sky Sports, Klopp elaborated on Liverpool’s fatigue levels after the fast-paced opening spell.
He said: “[It was a] super football game to be honest.
“Two top teams ready for a massive fight – energy levels of both teams incredible.
“You could see after 10-15 mins everybody breathing [heavily]. I’m really happy – City’s lowest number of chances against us.”
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