Alan Pardew's men twice held the lead on Saturday, Remy opening his account with a double, only to be pegged back by Steve Bruce's men on both occasions, before Sone Aluko clinched victory for the newly promoted club.
Remy, on loan from Championship side QPR, was disappointed that Newcastle were unable to press home their advantage and accepted his share of the blame after failing to complete his hat-trick in the dying seconds, volleying wide from point-blank range.
"I am a striker. For me it is frustrating when I miss that type of chance," he said.
"I should have scored. I should have kicked it with my left foot. I didn't do that. I missed it, so it is disappointing.
"I'm happy with my goals but the most important thing is to win the game and we didn't do that.
"We made too many mistakes and that was why we lost. We have a couple of games coming up this week and we need to be better.
"We have done very well in the last two games, but we are very disappointed because at home it is important we win for the fans and for the confidence.
"We didn't do that and that's why the gaffer spoke to everyone afterwards to say we have to win at home"
Still, despite that setback, Remy believes that Newcastle can challenge in the higher reaches of the division.
"I think we have good quality in this team, we can finish near the top in this league," he added. "We have to win this type of game to have a chance of that though.
"It's a good team here. It's all about adapting to each other and I know that some of the players here all have quality. I know we have a good group.
"It is a responsibility for us to respond well. We have to go to Everton and win and we have to also win in the cup."
