Lallana sustained a thigh injury during England’s win over Lithuania but still managed to play all 90 minutes, having completed just over an hour of the friendly meeting with Germany four days previously.
Klopp has no issue with Southgate, who called the Liverpool manager this week to explain his decision to field Lallana in the World Cup qualifier at Wembley.
“I think it is absolutely normal to have contact with the manager of the national team,” said Klopp.
“It is not about appreciating [the call] it is about the normal situation. We both share players.
“Of course I was not happy—someone said I was ‘relaxed’ about the situation but I could not be less relaxed about this, but it is not about blaming Gareth Southgate.
“I was not happy that he played on Wednesday but it is not my decision and I respect 100 percent the decisions of other managers because they have to respect my decisions, too.
“[Lallana] made the lineup [against Germany] and he loves football that much he obviously didn’t say, ‘I should maybe wait another day’.
“I really think we could handle these situations better if we work together.
“As long as we do not work together we will have these situations all the time.