The 22-year-old Brazilian midfielder scored only his second goal since joining in 2007 to bring United level after the Spaniards had taken a first-half lead through Pablo Hernandez.
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United needed to avoid defeat at Old Trafford to win the group and peppered the Valencia goal with chances before their hopes of becoming the first team to go through the group stage without conceding were dashed with the opener.
Dimitar Berbatov, who scored five goals in United's 7-1 win in their last Premier League match against Blackburn Rovers, threatened to open the floodgates again but saw chances from his head and feet repeatedly blocked by keeper Vicente Guaita.
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"Berba could have scored another five," Manchester United manager Sir Alex Ferguson told a news conference. "He was unlucky, the goalkeeper made two great saves from him.
"We played a lot of good football, we had a lot of good chances. I was pleased the penetration of the team was good but I just felt that about five minutes after we scored the goal, and we should have gone 2-1 up in that time, we started to settle for what we had and that is always a dangerous game. (It was) a lack of experience in the back there."
Ferguson had fielded the 20-year-old Da Silva twins, Rafael and Fabio, on either side of experienced central defenders Rio Ferdinand and Nemanja Vidic. Ferdinand went off just after half-time with a tight hamstring and was replaced by 21-year-old Chris Smalling.
SWIFT BREAK
After a bright start by two teams who had already qualified for the next round, United went behind when midfielder Pablo Hernandez slotted home in the 32nd minute after a swift break.
Young home keeper Ben Amos, a surprise name on the team sheet, was beaten after the midfielder was set up by Alejandro Dominguez after United's Michael Carrick lost possession in midfield.
There was plenty of action from regular goal scorers Nani, Wayne Rooney and Berbatov to keep fans warm on a freezing night at Old Trafford, where the match officials wore leggings and every player's puff of breath was visible in the air.
Despite an offside goal for Berbatov and a shot against the crossbar for Rooney, it was Anderson who came to United's rescue when he mopped up after Guaita had parried Park Ji-sung's shot.
He should make more of a habit of it, said his manager.
"He should get more (goals), yes," said Ferguson, whose team had eight attempts on target and nine off. "He has got terrific talent the boy. Great pace and power, a strong boy. But I'm pleased he got a goal, it may help him."
Some of Valencia's best first-half chances came from striker Dominguez, whose curling right-foot shot from just outside the penalty area was heading for goal before Amos smothered it and he also cracked a shot against the post.
"I think we competed well, the draw was a fair result," Valencia manager Unai Emery told a news conference. "We had a lot of the ball but I think the chances they created made it a fair result."
