"Their keeper made a couple of great saves but from the first-half we could have been a couple more up," the Ireland defender said. "Overall though we have to be happy. We are more than capable of scoring an away goal at the Emirates but it is far from over."
Arsenal boss Arsene Wenger admitted he had been relieved to see his side concede only one goal but insisted they could turn things around at the Emirates next week.
"Almunia kept us in the tie and we want to take advantage of that," the Frenchman said. "But it is very balanced. We still believe we will do it at home and you will see a different Arsenal next week."
Carlos Tevez's decisive role in the weekend comeback against Tottenham earned him a place in a United starting line-up in which there was no room for either Dimitar Berbatov or Ryan Giggs, who was made to wait until 66 minutes had elapsed before coming on to make his 800th appearance for the club.
Arsenal's defensive problems were eased as former United centreback Mikael Silvestre and teenage leftback Kieran Gibbs both came through late fitness tests, although the opening exchanges hardly inspired confidence in a back four missing both William Gallas and Gael Clichy.
Within two minutes, Darren Fletcher's cross had given Wayne Rooney the chance to force Manuel Almunia into a fine one-handed save and it quickly became apparent that Arsenal would struggle to cope with the tempo of United's opening salvoes.
A superb double save from Almunia denied Tevez just after quarter of an hour had elapsed but the resulting corner saw the holders claim the opener that their efforts deserved.
The initial delivery failed to trouble the Arsenal backline but, fatally, Michael Carrick was allowed to pick the ball up beyond the back post and hook it back across goal.
Theo Walcott's attempt to intercept only served to direct the ball into the path of O'Shea and the Ireland defender finished with the aplomb of a seasoned striker, hitting a half-volley into the roof of the net.
Still reeling from that setback, Arsenal were fortunate not to concede a second when Cristiano Ronaldo headed an inviting cross from Tevez straight at Almunia.
But as the first half came to a close, the visitors began to string a few passes together although there were no clear chances to show for their attractive build-up and Almunia had to be quickly off his line to deny Ronaldo after a slipshod passback by Gibbs.
With United's energy levels slipping, chances were thinner on the ground after the interval, but the hosts were still unfortunate not to double their lead with just over 20 minutes left after a piece of brilliance from Ronaldo.
Picking up a loose ball just inside the Gunners' half, the Portuguese winger advanced to within 30 yards of the goal before unleashing a wickedly dipping drive that left Almunia completely stranded but clattered against the bar.
By that stage, Giggs had entered the fray and the frustration of the evening for United was summed up by the fact that only a fractional offside decision prevented the veteran Welsh winger from marking his landmark appearance with a goal.
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