Shaqiri was born in Kosovo, an ethnically Albanian province that fought a war of independence against Serbian-dominated Yugoslav forces in the late 1990s. The Serbian government refuses to recognise Kosovo's independence.
Klopp opted against taking the attacker to Belgrade for Tuesday's Champions League clash and said Shaqiri had accepted his decision.
"I took a lot of times in my life a decision about a playing squad, a travel squad, and so far the player's always accepted it," he told a news conference.
"We come here as a football team and we represent one of the biggest football clubs in the world. That's why we're here, to play football. We want to focus on that, that's all.
"And because of the situation, people here all know better how the situation is, we decided not to bring Shaq here.
"And I said it, he's our player, he will play a lot of games for us but not [on Tuesday], that's all."
Liverpool thrashed Red Star Belgrade 4-0 last month and top Group C by a point heading into the clash.