Kenny Dalglish took charge if his first game after his return as Liverpool manager on Sunday, but he could not prevent an FA Cup third-round defeat to Manchester United, dpa reported.
Ryan Giggs got the only goal with a controversial early penalty, but Liverpool showed greater resolve than in recent weeks, even after the 32nd-minute dismissal of Steven Gerrard.
Dalglish's return could hardly have got off to a worse start, as Daniel Agger was deemed to have tripped Dimitar Berbatov in the box after 31 seconds.
There was contact, and the award was probably justified, but Berbatov's reaction was delayed, and Liverpool's players were furious at the award from referee Howard Webb.
Pepe Reina went the right way, but Giggs's penalty was firmly struck and flashed past his dive into the corner.
Liverpool rallied after that, and were purposeful if not exactly threatening, but their hopes of forcing an equaliser were hit when Gerrard was sent off for a lunging foul on Michael Carrick.
United, as so often this season, weren't particularly fluent, arguably were the poorer team when it was 11 against 11, but they almost doubled their lead in first-half injury time as Jonny Evans headed a Giggs corner against the post.
In a game of little fluency, United struggled to find a second goal to kill the game off. Reina saved from Evans and Berbatov in an astonishing scramble, but clear chances were a rarity.
United, though, were never really threatened, and while Liverpool could draw encouragement from a combative performance, this was a comfortable win.
League One Charlton Athletic held out for 49 minutes away to Tottenham Hotspur, but fell behind to debutant Andros Townsend.
Two goals in rapid succession from Jermain Defoe sealed a 3-0 win.
Chelsea play Ipswich Town and Leicester City host Manchester City in the day's later fixtures.