Referee Anthony Taylor adjudged Adrian fouled Liverpool left-back Flanagan for the match-deciding spot-kick, but the goalkeeper thought he got the ball.
"I thought it was the wrong decision because I touched the ball with my hand and I think Flanagan did not claim anything on the pitch," said Adrian on whufc.com.
"I think it was a bad decision from the referee.
"We didn't lose this match because of our performance, because it was a good performance. One point would have been good for us but finally we lost.
"Decisions are made in the moment and I think this decision was very bad for us."
West Ham next play Arsenal next Tuesday night, with the Hammers targeting victory.
"It's a good game for us," Adrian added. "We have to go to the Emirates with confidence and put in a good performance.
"We need more points because the Liverpool match was bad for us (in terms of the result)."