Rafa Benitez reacts to Newcastle's draw '“ and Sunderland's victory
After a dismal first-half performance, Jack Colback, Aleksandar Mitrovic and Georginio Wijnaldum all failed to converted second-half chances at Villa Park.
Sunderland, meanwhile, came from behind to beat Chelsea 3-2 at the Stadium of Light.
Sam Allardyce's side – who have a game in hand and a superior goal difference – are now a point ahead of United.
And Sunderland could relegate 18th-placed Newcastle with a win over Everton at the Stadium of Light on Wednesday night.
"We are disappointed," said Newcastle manager Benitez, whose team end their campaign with a home game against Tottenham Hotspur on May 15.
"Sunderland won, so all we can do now is wait for the score of that game and now try to win our game.
"We were a little bit anxious in the first half. We were not comfortable in possession. You have to take your chances and we didn’t do that.
"We had to change things in the second half. We did that, but it was not enough. The players are disappointed. "It was an opportunity to stay ahead of Sunderland, and we couldn't do it."