Manager Ange Postecoglou told David Turnbull not to cap his ambitions after the midfielder scored his first career hat-trick in Celtic's 6-0 thrashing of 10-man St Mirren at Parkhead.
Liel Abada opened the scoring in the 17th minute and by the time the 19-year-old winger had headed in a second five minutes later, Saints midfielder Alan Power had been given a straight red card for a foul on 22-year-old Scotland international Turnbull, who grabbed a double before the break.
Odsonne Edouard added a fifth in the 62nd minute and the former Motherwell player completed his hat-trick in the closing stages.
"Yeah, even before I arrived, David had an outstanding year last year," said the Hoops boss, who responded to speculation linking him to Hibernian striker Kevin Nisbet by saying "that is in the basket of uncertainty that I don't really dip my hand in".
"He has all the ingredients, physically, he works hard, great technique, good temperament.
"The challenge for David is not to put any limits on the player he can be and the levels he can reach.
"That is my role and the staff's role to keep pushing him.
"I think he gets frustrated by himself sometimes when he is not scoring or assisting but I think there is more to his game than that and once he adds those other things he will keep improving and where that takes him it will be up to him.
"You may say that I'm a little bit arrogant to say that we are going to improve after we won 6-0 but we are still at the beginning of what we are trying to build.
"There is definitely going to be challenges along the way, what happens after days like today and the run we are on, is that players get encouragement and they want more.
"It is my responsibility and the staff to keep pushing him (Turnbull) to levels and that's what it is all about, not to be complacent or satisfied with where you are at."
While side-stepping the question about Nisbet, Postecoglou freely discussed Croatian defender Josip Juranovic who agreed a five-year deal from Legia Warsaw.
He said: "I am really pleased to get Josip in.
"He is one we have been working in for a while, he is exactly the kind of player and person we want in our dressing room and I am sure he will help us.
"We will keep chipping away and hopefully get the ones we have been working on for a while now."
Speaking about Power's red card and striker Curtis Main being flagged offside when he got the ball in the net, St Mirren assistant manager Lee Sharp, in charge with manager Jim Goodwin absent after testing positive for Covid-19, said: "Alan should possibly stay on his feet. He doesn't have to go to ground.
"But I've seen tackles like that given as yellow cards. A few moments later, (Ryan) Christie had one on (Ethan) Erhahon that was very similar on the far side.
"He wasn't even booked so you're just looking for it to be evened up.
"Big decisions went against us. At 2-0 down we were trying to get ourselves back in the game and we got a goal chalked off that was perfectly fine, onside.
"I'm not saying we would have got anything from the game but at 2-1, the boys would have got a lift and a bit more belief."
