The Magpies found themselves 3-0 down at half time on Merseyside before goals from Yohan Cabaye and Remy gave them a glimmer of hope.
However, the visitors were unable to grab an equaliser as they suffered their third loss of the season.
"It was a long journey last night for them," Remy told the Newcastle Chronicle. "The group is disappointed as much as them but the fans still supported us all the game.
"We heard them a lot in the second half. They continued to support the team. I'm sure we'll do better at Cardiff [City[ for them."
Monday's defeat has seen Newcastle slip down to 16th place in the Premier League table after six matches.