Rhinos kicked off their pre-season campaign with a 10-4 win over Wakefield Trinity in the Wetherby Whaler Festive Challenge on Boxing Day after they had trailed 4-0 at half-time.
Briscoe scored Leeds’ opening try, which levelled the scores with 18 minutes to go, before Ash Handley crossed for the winner soon afterwards.
He felt it was an encouraging way to start their warm-up games.
But also highlighted how much still needs to be done before their Betfred Super League opener at Warrington Wolves on Saturday, February 2.
“The signs are there that we’re going to have a strong season,” Briscoe said.
“We’ve had a good pre-season, the boys who’ve come in have all fitted in well and it’s looking positive.”
Rhinos, without seven senior players, defended well under sustained pressure, but some poor handling let them down close to Trinity’s line.
Reflecting on the game two days ago, Briscoe added: “In patches we showed what we’ve been practicing in training.
“I thought for the majority of the game we scrambled for each other and defended really well. They just got one try from an error by us, we didn’t react quick enough on our side, but attacking-wise we’ve got a bit to work on.
“It was good to get the win though, in the first game.”
Despite managing only two tries, Briscoe insisted Rhinos will look to attack in 2019.
He stressed: “We’ve been working on that, on our attack and trying to challenge teams.
“Hopefully the more games we get under our belt the more fluent we will become.
“I think the more games we get together and the more time spent in training, the better we’ll be.”
Briscoe was one of Rhinos’ few success stories last season, scoring 18 tries in 33 appearances and signing a new contract which will keep him at Leeds until the end of 2020.
“I am happy,” he said of his efforts in training so far.
“I feel like I’ve had a good pre-season and just kicked on from last season really.
“Hopefully I can carry that on into the new season.”
Rhinos’ players have been given some time off after Christmas, but will resume training on January 2.
Their next pre-season fixture is at Doncaster on Sunday, January 13.
They visit another Betfred League One side, Coventry Bears, five days later before taking on Castleford Tigers in Kallum Watkins’ testimonial game at Emerald Headingley on Sunday, January 20.
Rhinos visit Featherstone Rovers for their final pre-season game on Sunday, January 27.
They also take on Hunslet at South Leeds Stadium in the annual Harry Jepson OBE Memorial Trophy tie the day after their league opener.