Despite suffering their biggest opening day loss in the top flight since 1937, the Reds' boss was pleased with the effort his players showed after being reduced to 10 men.
Liverpool manager Brendan Rodgers felt aggrieved after his side lost 3-0 to West Brom, claiming that the two home penalties and the sending-off of Daniel Agger were "very, very harsh."
Zoltan Gera's spectacular volley was all that separated the two sides at the break, however two spot kicks, one of which the Baggies scored, as well as a red card for the center back saw the hosts dominate the second and net a third through Romelu Lukaku.
Shane Long went to ground under pressure from the Dane for the first penalty, which saw him dismissed, however replays suggested that there was minimal contact. Martin Skrtel conceded a second minutes later, in a second of decision that Liverpool was unable to recover from.
"I thought we had a couple of decisions that were harsh on us,” Rodgers told Sky Sports News. "After the first five or 10 minutes we got good control of the game and got into a good rhythm, [we] created a couple of chances and looked like we just were ready to break the deadlock at any time.
"We then concede a corner and to be fair to Gera it's wonderful technique. There's not much you can say, Martin Skrtel's got a good header on it, Glen Johnson went to press the ball but it's wonderful technique and a great finish.
"From being largely in control the first-half we went in 1-0 behind. We made a good start to the second-half, but then we had a couple of decisions go against us. But we're not going to get everything our way, we've got to accept it. Pepe [Reina] made a great save from one of the penalties. When you see the close ups of the sending off and penalties they're very, very harsh."
Reds' fans hopes were momentarily lifted when Long's weak penalty was saved by Reina. However, two minutes later Odemwingie blasted the second spot kick past the Spanish keeper and the game was over.
Despite the obvious disappointment the 39-year-old was pleased with the determination his players showed when being reduced to 10 men.
"It's always difficult then, you're 2-0 down and you've got a man down and you lose structure to your team," he added. "I've got to give players credit, the score was 3-0 but they never stopped, they ran themselves to a standstill, and I can’t ask any more than that.
"We'll have days along the way and it will hurt, and it will be difficult for us, but I can't ask any more from them in terms of commitment and effort. When you go a man down at this level it's very difficult and so early on in the second-half."
Liverpool scored just nine percent of total attempts on goal last season, the worst return of any Premier League side. Its finishing was just as suspect on Saturday with Luis Suarez in particular guilty of squandering a number of chances.
The Reds' boss acknowledged that they need to sharpen up in front of goal if they are to progress, while congratulating opposite number Steve Clarke for recording a victory in his first Premier League game with his new side.
"There's no doubt that's the reality, we need to score more goals," he said. "We had half chances, Luis [Suarez] had a great header in the first half, [we] worked the ball really well on the side, brilliant cross, [and it] looked like he was going to score. There's no doubt that if you're going to affect the top of this league you've got to score more goals.
"Today wasn't our day and congratulations to Steve [Clarke] it's nice for him in his first game to get a result. Hopefully for us we won't have too many days like that and we'll keep moving forward."