Anthony Stokes was praised by Celtic manager Neil Lennon after the striker's hat-trick removed the chance of Peterhead effecting a cup upset.
His goals put Celtic into Monday's fifth-round Scottish Cup draw but Lennon believes there is more to come.
He said: "He can tidy up his game. He's only a young man yet he's been around a while. He's got so much potential.
"He could have had six today. Some of his link-up play was not great but he always gets a chance in a game."
Celtic were seldom threatened against the Third Division strugglers and dictated play for much of the match at the packed Balmoor stadium.
Stokes tapped in Celtic's first after 36 minutes, then hit two after the break, while Ki Sung-Yueng crashed a shot against the crossbar.
"He is a goalscorer. He's a great lad and he's having a great season and we want him to continue that," added Lennon of Stokes.
"He creates a lot for himself. He worked really hard for the team today and it was a good all-round performance."
Lennon was also boosted by the eager performance of full-back Cha Du-Ri and, on the other side of defence, the return from injury of Emilio Izaguirre.
The manager said: "Cha kept stretching Peterhead down the right-hand side. We got the goal at a good time and after that we were in complete control.
"With better finishing we could have won the game more comfortably. I was really pleased with the performance.
"Once we found our rhythm we were fine.
"I thought Emilio was excellent and that will do his confidence the world of good.
"He has been back training for four or five weeks and we thought it was perfect timing to put him in. He came through it unscathed and we are very pleased."
Lennon confirmed that Southampton have made an enquiry about striker Gary Hooper but said that was "as far as it went", before adding that he was not looking to sell any players, "especially not my leading goalscorer".
Midfielder Joe Ledley was forced off with an eye injury and was replaced by Victor Wanyama but Lennon is confident the Welshman will be available to face Dundee United at Celtic Park on Saturday.
"He got a cut eye on the eyelid from an elbow which I wasn't altogether pleased with, but the referee deemed it to be accidental," said the Northern Irishman.
"He just got a little nick and he should be okay for the weekend."