Ruud van Nistelrooy's missed penalty capped a disappointing night for a Manchester United side who badly missed the influence of injured star Wayne Rooney.
Van Nistelrooy saw his second-half spot-kick saved by Boro keeper Bradley Jones to condemn United to a second successive goalless draw on home soil.
The hosts now need a last-day victory over Charlton to be certain of claiming runners-up spot behind Chelsea and an automatic place in next season's Champions League. Without Rooney there is no guarantee they will get it.