The Reds were part of 12 clubs who launched their own European competition, which drew widespread and intense criticism from media pundits, former players and even their own supporters.
Klopp and his players were booed and jeered by fans ahead of their Premier League game at Leeds on Monday night, which ended in a 1-1 draw.
But the German insists he will not walk away from the club during a tough period.
Asked if he felt let down by FSG, he said: "I don't think that, I don't feel that. I am 20 years in football, and a lot of times owners made decisions without asking me, and I deal with it. I don't want to be involved in these things, I don't understand them. I'm a football person. It's not about letting me down.
"I'm here as a football coach and manager, and I will do that as long as people let me do that. I heard today that I will resign or whatever.
"If times get even tougher, that makes me even more sticky that I will stay here. I feel responsible for the team, responsible for the club and for the relationship we have with our fans. It's a very tough time, but I will try to help to sort it somehow."
He added: "I am at the club six years, around about. I know our owners, they are serious people, reasonable people. They care about us.
"But they never had to explain these kinds of decisions to me or ask me for permission. That's the situation. I speak a lot to them, but I was not involved at all in the process. I got the information yesterday.
"The English system is like this, there is pretty much one voice in the club and that's the manager. It's different to Germany. But there will be a moment for sure when our owners say what they have to say. Definitely, I'm sure."