The Reds were beaten 2-1 at Upton Park on Tuesday evening.
The Reds were unfortunate losers in the fourth round replay at Upton Park on Tuesday, with a header from defender Angelo Ogbonna late into added on time sending the Hammers through.
Jurgen Klopp’s side had been more than competitive in the game though, with them having had several big chances to secure progression themselves.
And Ilori has heighted the positives saying that they didn’t receive the result that their performance on the night had deserved.
"There are always positives and I definitely think the way we played, the opportunities we made, the way we fought, they're all positives," he told Liverpoolfc.com.
"We didn't get the result we think we deserved and the one we fought for, but that's football.
"We worked hard, we managed to make some clear-cut chances and opportunities to score goals, but we didn't make the right decisions at the right times."
Liverpool will now be hoping they can turn their attention to the Premier League after their exit from the FA Cup.
They are currently ninth in the table and just four points away from West Ham in sixth and six points behind Manchester United in fifth.
That demonstrates a place in Europe is very much up for grabs, and they will be keen to secure one of those top six spots in the remaining 13 games of this season.