The Belgian, 29, now fears for his place in the Red Devils' squad for Russia this summer if he continues to play second fiddle to 24-year-old Loris Karius.
Mignolet insisted: "I will soon be 30, and the World Cup finals are coming around. My current situation clearly can't continue much longer.
"I know he has a lot of faith in me, and I played well in the recent friendly against Japan.
"But it is always important for me to be playing matches.
"I always try to keep calm, and I have come back stronger from similar situations in the past.
"But of course I have to think about my own future. All I can do is focus in training and do my best.
"Klopp then told me what was going to happen for the Manchester City game. Of course I was not happy, although no harsh words were said.
"He told me honestly that Karius is ahead of me in the pecking order. I am absolutely not happy with this, although I always have to respect the coach's decision.
"After all that has gone on this season, I now know where I am - and the situation has become clearer.
"I have captained the side three times this season. I asked for an explanation to the bizarre situation after the Burnley game.
"I had a premonition about what might happen with me - and it turned out to be correct."