The 26-year-old Frenchman, the only new face added to the Magpies' squad during the summer transfer window, lit up St James' Park with a first-half double against Hull.
However, he headed home on Saturday evening bemoaning the one which got away after passing up a last-gasp opportunity to complete a hat-trick and snatch a Barclays Premier League point as the Tigers staged a concerted fightback to win 3-2.
Asked if his brace would be the first of many goals during his season-long loan spell, Remy said: "I work for that.
"I think I can score a lot of goals here for the fans, for the club and for me.
"I scored two goals, but I'm not finished yet. I can score a lot of goals here.
"I try to do my best in every game. I scored two goals, but it wasn't enough, so I will try next game to work hard again and hopefully we can win."
It took Remy just 11 minutes to demonstrate his prowess in front of goal when he headed home from close range after strike-partner Papiss Cisse had scuffed a volley in his direction from Moussa Sissoko's cross.
But as the home crowd settled down in anticipation of a comfortable victory, the Magpies took their foot off the gas and Hull eased their way back into the game.
They levelled with 26 minutes played when Robbie Brady ran on to Sone Aluko's pass and fired through goalkeeper Tim Krul's legs.
Newcastle responded and edged their way back in front a minute before the break as Remy reacted first to fire past Allan McGregor after defender James Chester had blocked Yohan Cabaye's shot.
But the home side succumbed once again within three minutes of the restart when former Sunderland winger Ahmed Elmohamady met Brady's free-kick unopposed to glance a header home off the inside of the post.
Worse was to come 14 minutes from time when the impressive Aluko thumped home a volley off the same upright, although Remy might have made it 3-3 in injury time as the ball flew across the Hull penalty area, but stabbed his effort wide of the target.
He said: "I work hard on the training ground to be good in front of the goal, but I am very frustrated because I missed the last one in the second half.
"I wanted to kick the ball with my right foot, but the right choice would have been to kick with my left foot, I think."
Manager Alan Pardew later admitted his side had been too loose and had contributed to their own downfall with the kind of defending he hoped had been eradicated since the 4-0 opening mauling at Manchester City.
However, he was at least able to console himself with Remy's contribution.
Pardew said: "That was probably the highlight for us because you can see he has got goals in him.
"I thought his all-round performance was good. As an individual, he can really give us a boost, but it's the team that needs to be stronger.
"We need to function better than we did on Saturday and hopefully we can do that."
The Magpies return to action in the Capital One Cup third round on Wednesday evening when they host Leeds before a difficult league trip to Everton at the weekend.
Remy said: "The best thing is that we don't have to think about this game for a long time because we play on Wednesday, so we have to forget this game and be concentrated on the game that's coming.
"Then we play away against Everton. It will be hard, but we can do it, I am sure we can do it."
Midfielder Cabaye limped off with a groin injury 17 minutes into the second half, but Pardew is hopeful there is no lasting damage.