Ex-Leeds and England captain Sinfield, now the Rhinos’ director of rugby, said: “You’ve seen over the past 10 months or so what Rob means to our club and our sport.
“The support he’s had from everywhere has been unbelievable.
“If he’s watching at home, and I’m sure he is, this is for you pal.”
Leeds were 12-6 in front at half-time but Salford fought back with tries from Pauli Pauli and James Greenwood to lead for the first time in the match.
However, Ash Handley’s second try of the final brought the two sides level and Gale kept his nerve with four minutes remaining to land the match-winning one-pointer.
“It was a tough game to play in,” said 32-year-old Gale, who returned to Leeds at the start of the 2020 season after coming through the club’s academy.
“I thought we were in control but then in the second half a bit of anxiety crept in.
“I thought we’d thrown it away at one point, and credit to Salford as they came back strongly in the second half, but we played terribly in the second half.
“There have been a few one-pointers this year and thankfully it went our way this time.”
‘As low as I’ve felt in rugby’
Salford played their part in a closely-fought final, but fell just short of their first win in the competition since 1938.
It meant more Challenge Cup disappointment for experienced Red Devils half-back Kevin Brown, who has appeared in four finals for four different teams and lost on each occasion.
The former England international, 36, said: “I’m proud of how much energy and effort we’ve put into it, but it’s probably as low as I’ve felt in rugby, coming up just short after having so many chances to win the game. I’m playing them over in my head. It’s heartbreaking.
“It’s the bounce of a ball, a referee’s call, that’s how close it was.
“We had five clear opportunities and blew them all. If we take one of those, we’re going home as winners.”
Salford also lost in the Super League Grand Final last season, but Brown is convinced that the club is on the right track in their bid for major silverware.
“There’s not much that Salford need to change,” he added. “It’s just so disappointing to come so close but go home as a loser again.”