While manager Alex Ferguson appeared satisfied to take a slender advantage to the Emirates, defender Patrice Evra said the players were disappointed they had not buried the Gunners at Old Trafford.
"We're happy about the way we played but we deserved more goals and we could have won 4-0, that would have been normal," the France international told the BBC.
"Now we need to focus on the away leg. We can score anywhere which is why I'm confident. The target before the game was to win and keep a clean sheet but the way the game was nobody was happy with 1-0 - we wanted more goals.
"We are very disappointed, believe me. We should have made sure the tie was over. We should have scored at least two more goals. We are not even thinking about Rome."
The semi-final, the first European meeting between the Premier League rivals, is delicately balanced, especially as Arsenal have not conceded a goal at the Emirates in this season's Champions League.
The Gunners also have the advantage of being able to focus fully on Tuesday's second leg and will rest players for this weekend's league game against Portsmouth, safe in the knowledge that a top-four place is all but assured.
United, in marked contrast, travel to Middlesbrough for a lunchtime kickoff on Saturday knowing that a slip-up could allow Liverpool back into the title race.
Arsenal manager Arsene Wenger promised an all-out assault on United in the second leg.
"There is a final at stake," Wenger said. "Don't worry, when you play at home knowing you could reach a final, we will be up for it. I am confident because I believe we will be on top next Tuesday and you will see a different Arsenal team."
United are waiting to hear the results of an X-ray on Rio Ferdinand's ribs. The defender went off near the end and if they are broken he could be out of action for two or three weeks.
