The visitors had early chances but Enner Valencia and Pedro Obiang were unable to find a way past Simon Mignolet.
Joao Teixeira, Cameron Brannagan, Joe Allen and Christian Benteke had chances for the Reds but an inexperienced Liverpool side were unable to find a winner.
The result means that the two sides will meet again in a replay at Upton Park in London next month.
And Owen feels that the Hammers will probably be the favourites to progress to the next round after Saturday’s draw.
Speaking on BT Sport after the game, Owen said: “If Jurgen Klopp thought [Liverpool] were the underdogs going into the game, they certainly are now because at Upton Park it’s going to be pretty difficult for them.
“You could say he doesn’t want an extra game, but if he’s going to play some of the young lads it’s quite a good experience for them.”
He added: “I thought West Ham were poor. If anything, Liverpool deserved to edge it.
“But even Liverpool didn’t create enough chances and I thought 0-0 probably summed up the game.”
Liverpool now turn their attentions to their Premier League clash with Leicester City at the King Power Stadium on Tuesday night.
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