The striker only made a limited impact after signing from Motherwell for £450,000 in January.
First-team chances were few and far between for Moult, who made only four starts and seven appearances from the bench.
His two goals both came as a substitute, including on the final day against Burton.
Bryson, who captained the Lilywhites in the 1995/96 Third Division title-winning season, thinks there is more to come from Moult.
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“I don’t think that we have seen the best of Louis Moult yet,” Bryson told the Post.
“So perhaps we should be reserving a bit of judgement.
“He came with an injury, which didn’t help. Louis was signed from the Scottish Premiership so it was a step up coming here.
“I’m a Scotsman saying that and accept the standard up there isn’t what it might be.
“He needs to be given a chance to show what he can do with a pre-season under his belt.
“Players take time to settle when they move clubs, some longer than others.”
North End are on the lookout for another striker this summer, in addition to Graham Burke who is set to arrive from Shamrock Rovers.
Currently they only have Sean Maguire and Moult who are out-and-out frontmen.
Bryson was impressed with what he saw from Preston last season and sees no reason why they cannot challenge for the play-offs again.
“I class myself as a PNE fan and they did well last season,” said Bryson.
“If they can add one or two more to strengthen the squad, I’m sure they can be right in the thick of it.
“I thought last season was a very satisfactory one when you consider the stature and budgets of some of the others in this league.
“There were a lot of players who impressed – Alan Browne had an outstanding season.
“Browne made sure he was one of the first names on the teamsheet.
“Ben Davies was excellent too. He was given his chance and showed what he could do.
“I think these are exciting times for Preston, they are not far away from a team which can play most of the season at the top end of the league.
“They can be right there in the mix and that would be great to see.
“When you look at what they might need, you would think of a striker with a bit of stature to hold the ball up.
“Maybe they need another centre-half or a right-back as cover.
“They’ve done some good business so far with the new contracts, making sure the core of the squad remains.”