Holders Chelsea had no such trouble, however, routing Hull City 4-0 away to record the club's first victory under new manager Avram Grant following Jose Mourinho's exit a week ago.
"It could have been better, it could have been 5-0," Grant told the BBC. "I was happy with the performance of the players. These kind of games you make one mistake and you are out.
"All the goals came from combinations and that's what I want from the team....they all enjoyed it, including me."
Manchester United were not the only top flight casualty as Martin O'Neill's Aston Villa lost 1-0 at home to his old club Leicester City -- Matthew Fryatt scoring the winner.
In other third-round ties, West Ham United scraped through 1-0 against Plymouth Argyle with a late strike by Dean Ashton and James McFadden scored twice as Everton won 3-0 at second division strugglers Sheffield Wednesday.
Tottenham's under-pressure manager Martin Jol got some relief when his side beat Middlesbrough 2-0 at White Hart Lane with late goals from Gareth Bale and Tom Huddlestone.
Blackburn Rovers also eased through with a 3-0 home win over Birmingham City. In another all-Premier League tie Bolton Wanderers won 2-1 at Fulham after extra time.
United manager Alex Ferguson sent out a youthful side at Old Trafford and Coventry, backed by 11,000 travelling fans, took full advantage to repeat the feat of Southend United last year.
Maltese striker Michael Mifsud slid in after 27 minutes to put Coventry ahead and doubled their lead midway through the second half to seal victory for the Midlands club.
Chelsea's Israeli manager Grant included plenty of seasoned internationals at Hull but it was 18-year-old Scott Sinclair who opened the scoring after 36 minutes.
Goals from Salomon Kalou and Steve Sidwell, his first for the club, just after the break effectively killed the tie before Kalou grabbed his second of the night in the 81st minute.
It ended a run of four games without a win for Chelsea although there was concern for winger Shaun Wright-Phillips who limped off with a leg injury.
The fourth round draw is on Saturday.
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