The Belgium international, who joined the Reds from Sunderland this summer, made a double save from Jon Walters' last-gasp penalty to earn Liverpool a 1-0 victory over Stoke on the opening day of the Premier League season.
Mignolet said: "There is an unwritten law in football that if you play well and don't take your chances, there will be chances for the opposition.
"I was thinking that, the longer the game went on. I had a feeling they would equalise in the last minute, really."
He added: "It was the debut that you dream of. I had hoped to do something like that, but you never really think you will. Saving a penalty in the last minute, on your first game for Liverpool.
"It can have a damaging effect if you play well and don't win. We can now go to the next game being relaxed that we can do the same things we have done, rather than feeling anxious that we have to win.
"It does change things. This time we won and that hasn't happened too often for Liverpool on the opening day of the season in recent years. This is very important to set our season off."