Danny Welbeck twice came close as United dominated the first half, but Valerenga could have stunned United when Ahmed Suleiman headed just wide after a swift counter-attack.
Wayne Rooney cleared off his own line to deny the home side in the second half, with replays suggesting the ball may have been over.
United continued to spurn great chances as substitutes Javier Hernandez and Anderson both misfired late on.
Sir Alex Ferguson named a strong starting XI for his side’s match at a sold out Ullevaal Stadion, with Vidic starting his first game since twisting his knee during United’s Champions League match in Basel in December.
But it was a contest that look a while to reach full speed, with United dominating but not troubling the home defence.
United eventually opened Valerenga up when Welbeck exchanged a neat one-two with Rooney, but couldn’t get the ball from under his feet to shoot.
Looking to make amends, Welbeck came close with another effort moments later – forcing goalkeeper Lars Hirschfeld into a good save low to his right after the England striker let fly from 25 yards.
But as the half ended with a flourish, Valerenga crafted a chance of their own – only for Suleiman to head wide after a swift counter-attack had exposed Ferguson’s side.
Little changed after the break with United calling the shots, but Valerenga came closest breaking the deadlock when Chuma Anene’s shot was cleared off the line by Rooney – although replays indicated the ball may have crossed the line.
Shinji Kagawa’s introduction provided United with some added impetus, but even he was unable to change United’s fortunes in front of goal.
United could have won it when Antonio Valencia raced down the right wing and pulled it back to Hernandez, but the Mexican miscued his shot from close-range.
Anderson, another second half substitute, could have won it in injury time when he coaxed the ball towards the top corner – but it dipped the wrong side of the bar ensuring a goalless draw in the Norwegian capital.