Real Madrid won the game 1-0 to lift their 14th European Cup, but the night will be remembered for the unsavoury scenes outside the stadium.
UEFA blamed “fake tickets which did not work in the turnstiles” for the events that saw supporters held up outside the stadium.
Fans were targeted by tear gas as police tried to disperse the crowds.
“I couldn’t speak to my family yet, but I know the families had a real struggle to get into the stadium,” said Klopp.
“I heard a few things that were not good, not nice. Obviously it was pretty tricky out there but I don’t know more about it.”
In a statement Liverpool called for a “formal investigation” into the security failings.
“This is the greatest match in European football and supporters should not have to experience the scenes we have witnessed tonight,” added the club’s statement.
Once the action got underway, Liverpool failed to round off a spectacular season as the Reds were denied by a string of stunning saves by Madrid goalkeeper Thibaut Courtois.
Vinicius Junior scored the only goal of the game just before the hour mark when the Brazilian turned in Fede Valverde’s cross.
“When the goalkeeper is man of the match then something is going wrong for the other team,” added Klopp.
“We had three really big chances where Courtois made incredible saves.”
Despite the disappointment, Klopp called on Liverpool fans to take to the streets of the city on Sunday when they parade the League Cup and FA Cup.
The Reds also fell just short in the Premier League as Manchester City pipped Klopp’s men to the title by one point.
“I feel the pride already, but I saw I was the only one in the dressing room at the moment, the boys need a bit more time.
“These boys played an outstanding season. The two competitons we couldn’t win, we didn’t win for the smallest possible margin.”
Klopp believes his side will be back for more after reaching a third Champions League final in five years.
“The difference between now and 2018 (when Liverpool lost the final 3-1 to Madrid) is I see us coming again,” he said. “I wished it but I couldn’t know it.
“They have an incredible attitude, it’s a fantastic group and we will go again.”