Adam went down after a challenge from Rio Ferdinand, leading to a goal from a Steven Gerrard free-kick.
The Scot's tumble attracted questions over its authenticity, but Adam was quick to deny that he went down deliberately.
"Well, everyone has an opinion and I felt a touch," Adam said. "If I hadn't gone down I would have been clear through on goal so there must have been contact. That's the way I look at it.
"I felt contact when I went past Rio and that's the way it goes. I'm not that type of player. I'm not just going to go down easily.
"It was a foul and that is why the referee gave it and the goal was just different class. That is why Stevie is one of the best players in the world."
The draw with United puts Liverpool at 5th place in the Premier League table with 14 points from eight games.