West Brom stunned 10-man Liverpool with a resounding 3-0 victory to mark the start of the Steve Clarke era in style at the Hawthorns.
Liverpool had defender Daniel Agger sent off early in the second half and looked like shambles at the back in the final half hour.
Liverpool's day was summed up by striker Luis Suarez, who could have had a hat trick before Liverpool was swept aside after Agger's dismissal.
But for Rodgers, this was a reminder that there is much work to do before Liverpool re-emerges as a potent force.
West Brom took the lead after 42 minutes. Glen Johnson was booked for a foul on Odemwingie and, though Steven Reid's free-kick was deflected wide, the resulting corner led to the deadlock being broken.
The Reds were reduced to 10 men after 58 minutes when Agger pulled back Long just inside the box only for the Republic of Ireland striker's weak spot-kick to be saved by Reina.
But referee Phil Dowd awarded another penalty when he judged that Skrtel had tripped Long. This time Odemwingie took the spot-kick and hammered the ball past past Reina.
Rodgers said he thought both penalties were "very harsh."
"I don't think either was a penalty and Martin Skrtel doesn't even connect for the second one," Rodgers said. "With the first one, Long's pace has got him there. There is slight contact but I know Long well, how big and strong he is, and it was very harsh.
"With 10 men and then chasing the game, it becomes difficult."
But the first save of note came from Baggies keeper Ben Foster, who parried away a powerful 20-yard drive from Suarez after a weaving run.
The home side was fortunate to win a free-kick when Long stumbled over Skrtel, but Reid was unable to take advantage as his set piece was deflected wide.
Suarez looked sharp and turned inside Gareth McAuley before forcing another save out of Foster.
He should have scored after half an hour when heading over from the edge of the six yard box after attacking a Johnson cross.
Suarez's frustration boiled over in first half injury-time when he was yellow carded for dissent.
"(Suarez) is a wonderful player, a good man, world class and a winner and when it goes against you, it can be difficult," Rodgers said.
Liverpool started the second half on the offensive and Suarez floated a free-kick wide after being brought down on the edge of the box by Youssuf Mulumbu.
But the Baggies weathered the initial storm and doubled their lead from the second of two penalties awarded them in the space of six minutes.
Rodgers said Liverpool may consider appealing Agger's red card, saying: "It is something we will look at. It was very harsh."
Suarez later missed a golden chance when he shot over from six yards after Foster had dropped a Steven Gerrard corner.
To add to Rodgers' woes, substitute Joe Cole limped off with a recurrence of a hamstring problem.
But Albion was now carving chances at will and Morrison shot wide with the goal at his mercy before Lukaku put the icing on the cake for Albion after 77 minutes.
Mulumbu's shot was deflected into the path of Ridgewell and his lovely lob to the back post was headed in at the far post by the on-loan Chelsea player.
"We showed some signs of our quality but the penalties and the sending-off kills you, especially a new team coming together," Rodgers said. "But I've got to give big credit to the players. They ran to a standstill today and I can't complain. It is still a work in progress. It is very much a marathon we are in. This is the first game."
Clarke was unsurprised by the quality of his side's performance.
"I think I've been in the game long enough to know you enjoy these moments but you know there are different Saturdays to come," he said. "But the performance today showed these players are comfortable in the Premier League. They've been there for two seasons, they've finished mid-table both times, they know they can handle themselves at this level.
"I wasn't worried about the game. I knew it was a good game for us to start with, that there was more pressure on Liverpool than us and that proved to be the case. But I was really pleased with the way we played."
Information from Press Association was used in this report.