Rodgers endures dreadful Liverpool debut
The defeat was made more galling by a thumping 5-0 win at Queens Park Rangers for Swansea City, the team he left after devising a style of play that wooed a Liverpool hierarchy keen to return to the pass-and-move groove of the 1980s.
Arsenal manager Arsene Wenger had almost as bad a day as Rodgers, watching his toothless side held 0-0 at home by Sunderland in the week last season's top scorer Robin van Persie joined rivals Manchester United.
New strikers Lukas Podolski and Olivier Giroud had decent chances but never came especially close, as Arsenal supporters, fed up by high-profile departures and no trophies in recent seasons, were left fretting over another difficult campaign.
News at full-time of midfielder Alex Song heading to Barcelona hardly improved the mood in North London.
Rivals Tottenham Hotspur were also frustrated in a 2-1 defeat at Newcastle United, where ex-Chelsea boss Andre Villas-Boas's new charges hit the woodwork twice before Newcastle's Demba Ba netted to end a personal 14-game goal drought.
Jermain Defoe grabbed Spurs' equaliser, following up his own header on 76 minutes, but Newcastle's Hatem Ben Arfa soon converted a penalty after the Frenchman was brought down.
Despite the win for last season's surprise packages, Newcastle manager Alan Pardew felt aggrieved after being sent to the stands for prodding a linesman in the back and then failing to get the walkie-talkie working to communicate with the bench.
Liverpool fans, many of whom were upset by the American owners' treatment of Dalglish when he was sacked at the end of last season after finishing eighth, were in a much darker place as the promise of a Rodgers revolution began very badly.
A Zoltan Gera cracker just before the break, Peter Odemwingie's 64th minute penalty, and Romelu Lukaku's header sealed a famous opening-day win for new Albion manager Steve Clarke, Dalglish's assistant at Liverpool last term.
It could have been worse for five-times European Cup winners Liverpool had Shane Long not missed an awful penalty on the hour after Daniel Agger's red card for a push.
Rodgers felt the decisions for the penalties were harsh.
"From being largely in control of the first half we went in 1-0 behind. A couple of decisions went against us," he told Sky Sports after handing debuts to Joe Allen and Fabio Borini.
"I've got to give the players credit, it was 3-0 but they never stopped."
In typically hot weather for the first day of the English season, Arsenal's and Liverpool's woes quickly gave fans something to talk about along with refereeing controversies, goalkeeping howlers and smash-hit new signings in other games.
West Ham United's top-flight return was marked by a 1-0 win over Aston Villa and their new boss Paul Lambert, although Kevin Nolan's 40th minute goal had a hint of offside.