Manager Sir Alex Ferguson rued his decision to leave out striker Dimitar Berbatov and the creative skills of Paul Scholes were also missed in a turgid Group C opener in which United's best chances came from long-range efforts.
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Adding to the English side's gloom on a subdued night was a serious injury for winger Antonio Valencia, who left the field on a stretcher with a dislocated and fractured left ankle that Ferguson said could keep him out for the season.
The manager defended his line-up, saying he had wanted to try out players who had not started this season, but admitted selecting striker Javier Hernandez to partner the quiet Wayne Rooney, back in the team after a week in the media spotlight over his private life, had been a mistake.
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"It played Berbatov out... he's been one of our best players this season, that was a loss," Ferguson told a news conference referring to the Bulgarian forward who has scored in three of four Premier League games this season.
"His ability to create out of tight situations would have made a difference."
United dominated from the start but Rangers' gameplan of effectively having two lines of defence to penetrate worked well, leaving Darron Gibson's four long-range shots as the closest United came to a goal.
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Rangers manager Walter Smith, twice assistant to Ferguson, outwitted his former boss but said his approach was the only option and one borne of Scottish teams' inability to buy top players because of financial constraints.
How he wished he could have had Ferguson's luxury of choice for his line-up, although it was his less glamourous charges who will appreciate earning a point more.
"I'd be delighted myself if I had the problem that Sir Alex has. If you look at his team selection today, any one of their players would get into 80 or 90 percent of Premiership teams... Wayne Rooney would get into them all," he told a news conference.
"Scottish teams are not in the situation we were in however many years ago. We were able to compete to sign players from all over the British Isles, the top players, but we can't do that now. We have to find a way to succeed or nullify the opposition as best we can."
Rangers signed their first two players for two years in the last transfer window, Vladimir Weiss on loan from Manchester City, who was on the bench, and the ineligible Nikica Jelavic.
"It's very difficult for us to compete in the Champions League with the financial disparity that there is. UEFA have allowed a situation to develop that is totally wrong.
"Bigger clubs from smaller countries have been drastically affected by the lack of finance and it's very difficult to compete," said Smith.
"It's easier to defend than it is to actually create... I don't feel proud of the fact that we'll do it but there's nothing else left for us."
Rangers did not create much of their own, with lone striker Kenny Miller spending vast amounts of time half a pitch away from the rest of his team mates.
"We have to give credit to Rangers, they came here to salvage somethin
