Jeers were heard across Wembley as the anthem was played on Saturday afternoon, and FA chief Prince William did not receive a warm welcome from Liverpool supporters either.
Historical controversy surrounding the Hillsborough disaster at Government level and continued grievances towards the Conservatives have been cited as reasons for Liverpool fans booing the anthem for a number of decades now.
Speaking ahead of Tuesday's Premier League clash with Liverpool, Klopp has admitted that he "did not enjoy" the noise from Liverpool fans but believed that their reasons for doing so were understandable.
"Of course I have thoughts. The question is why does it happen? They wouldn't do without a reason," Klopp told reporters during his pre-match press conference.
"The majority of our supporters are wonderful people. Really smart, go through lows and highs. It was not something I enjoyed."
Kostas Tsimikas scored the vital spot kick for the Reds to propel them to their first FA Cup crown for 16 years after a goalless stalemate with Chelsea in the capital.
However, Klopp took aim at the FA for restricting the number of medals that can be awarded, and the German coach issued a passionate plea to the governing body to ensure the efforts of all of his players were rewarded.
"I cannot believe the amount of medals is restricted. The FA, please send some more medals. The squad gets bigger but the numbers stay the same," Klopp added.
"I love it that the boys came on and contributed. I know they contribute and it's nice if they can get the public reward as well. We can give all the boys the opportunity to show how good they are."
With a number of players also completing two hours of action at Wembley, Klopp has insisted that he will "have to make changes" for the battle with Ralph Hasenhuttl's side.
"This is game 60 so we have to be very careful. We don't finish the season tomorrow. When did Southampton have their last game? 10-12 days? Southampton are completely fresh. They are always a well drilled team," Klopp said.
"We have to make changes. I don't know how many. This process is not finished yet because we only played the 120 minutes two days ago.
"We have a lot of decisions. We will line up a team with one reason. To try and win the game at Southampton. We have to see who is able to help, the 30 extra minutes made a big difference. We will have to see."
Victory for Liverpool would see them cut the gap to Manchester City at the top of the table down to one point after the champions could only draw 2-2 with West Ham United at the weekend.
However, should Southampton overcome Klopp's side, City will officially be crowned 2021-22 Premier League champions with one game to spare. body check tags ::