The loss left Rhinos four points outside the top-six with only four rounds remaining in the Betfred Super League season.
There was doubt over at least one of Giants’ tries as they raced into a 16-0 lead and Smith was adamant the drop goal which put the hosts two scores clear in the final few minutes was wide of the target.
“We let ourselves down in a few moments,” Smith accepted. “One of the tries we conceded from a scrappy kick, we have got people walking in the background.
“The bounce pass in the other corner was a bit unfortunate, then there was a play where he [Giants Kevin Naiqama] looked like he was held.
“Maybe he was, maybe he wasn’t. Chasing points is difficult in games where the ruck is all over the place and some critical moments in the game were influenced.
“Even at the back end, we are chasing the game and the player that doesn’t get to his feet, laying on the ground, ends up retrieving our offload, when we are right in front of the posts.
“There was a stoppage in play when we made a break and we were about to score on the next play, we have a two-five-minute stoppage and then the player passes his hia [head injury assessment].
“There was a huge amount of spirit in the second half, we were trying to overcome everything, including a drop goal that didn’t go through. The kicker and his mates were all laughing, that it didn’t go through.
“They were getting ready for a 20-metre restart and a seven-tackle set. Everybody has said it didn’t go through, except the decision-makers.
“A couple of players in the opposition said it missed by a couple of metres. Sometimes they are difficult when you look over the goal posts and you’re not sure if it’s a high kick. In the end we had opportunities, but some days it is hard to overcome all those things.”
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It was effectively a must-win game for Rhinos after the sides immediately above then on the table all won earlier in the weekend.
“Every loss this year has felt like a massive blow and every loss ever in my life will be a massive blow,” Smith admitted.
“Certainly that makes it much harder, but mathematically we are still right in the picture. I haven’t looked at who plays who, but I’d imagine we need to win them all.
“You usually need to get one more win than losses - if you get to 14 wins in a 27-round competition you usually get there, but we just need to get one next week first.”
The first half of the game was overshadowed by an injury to Rhinos second-rower James Bentley.
Play was halted for more than 10 minutes as he was treated on the field, before being removed on a stretcher and taken by ambulance to hospital.
Speaking straight after the game, Smith said: “He is okay, he has regained consciousness.
“He was in a bad way there for a bit and he is awaiting a scan to check hisd head and neck, but the signs at this stage are that he will be okay.
“He was talking to the doctor prior to getting into the ambulance so it is precautionary, the medics are saying at the moment.”
Rhinos were without David Fusitu’a, who was ruled out because of a back injury.