Erik Karlsson, San Jose Sharks New York Rangers

SAN JOSE — James Reimer did what he could on Saturday to help the Sharks endure a long losing streak on home ice. But the skaters in front of him didn’t offer much support.

Julien Gauthier scored the 40th shot Reimer had made to that point at 1:57 of the third period as the Sharks went down 2-1 to the New York Rangers on Saturday in front of a predicted sold-out audience of 17,562 at the SAP Center lost .

The Sharks netted just four shots in the third period, including Logan Couture’s goal with 16.1 seconds left in regulation that helped his team avoid their first shutout of the season.

The Sharks are now 0-4-3 at home after beating the Toronto Maple Leafs 4-3 in overtime on October 27. This win remains the Sharks’ only win at the SAP Center as they now own a 1-6-3 record this season at the Downtown Arena.

Adam Fox scored an empty net goal for Rangers at 1:07 in the third period. Reimer finished with 41 saves.

Reimer made 15 saves in the first half, one more than in Thursday’s entire game against the Detroit Red Wings in the Sharks’ 7-4 loss that set up a three-game home stand.

Against the Red Wings, Reimer stopped 14 of 20 shots and just four of seven in the third period as the Sharks conceded the final three goals of the game after making an impressive comeback from a two-goal deficit.

Of Reimer’s 27 saves in the first two periods on Saturday, five came shorthanded as the Sharks converted all three penalties they took in the first 40 minutes. The Sharks started Saturday with the top power play in the NHL at 92 percent and took a 5-on-5 lead in their last meeting with the Rangers on Oct. 20.

In that game, Karlsson scored the winning goal in overtime and assisted the Sharks in the Sharks’ 3-2 win at Madison Square Garden, earning the team’s five-game slip earlier in the season. Including that win, the Sharks had a 6-5-3 record going into Saturday from a 0-5-0 start.

If the Sharks manage to get back into the playoffs, they may look back to an Oct. 19 practice session in New York as something of a turning point.

The Sharks were defeated 5-2 by the New York Islanders the night before for their fifth straight loss. The day before the game, coach David Quinn and captain Logan Couture sat down to discuss how urgent the team’s situation had become and how much better they needed to get from a training perspective.

“When we get out of here, when practice ends, you want to feel good about what you’re trying to accomplish with your mental and physical effort,” Quinn said. “But you have to see your teammates doing the same. This is the only way to gain team trust.”

Quinn said in his playing days, when he was training and not in a specific drill, he would watch and notice when passes weren’t being completed and/or when his teammates weren’t executing.

“When practice ended like that, I didn’t think our team was very good,” Quinn said. “So if you want to believe you’re a good team, you have to watch everyone do the right thing or try to do the right thing.”

The Sharks’ Oct. 19 practice marked a change of season of sorts, since they’ve at least been good enough not to fall further down the Western Conference rankings.

“I think it hit us right in the eye and we’ve just done a lot of things better since then,” Quinn said. “We trained better, we played better, we got better results. Not the results we want, but we got better results.”