The Scotland international was handed his Newcastle debut in the side’s EFL Cup tie against Blackburn Rovers at St. James’ Park on Tuesday.
Fraser, who joined the Magpies on a free transfer earlier in the transfer window, marked the occasion by scoring the match’s only goal and earning Steve Bruce’s side the win.
However, the 26-year-old was replaced by Jacob Murphy before the hour mark and Newcastle great Anderson believes the winger is still some way off being able to last the entirety of a match.
The 60-year-old is of the view that Fraser showed signs of tiredness half an hour into the game and believes he will be slowly eased into the team rather than rushing him into the starting eleven.
“He has stated that he has kept himself right and he has been training and what not, but you could see half an hour into the game that he was blown“, Anderson said on BBC Radio Newcastle.
“There is no substitution for game time, he’ll be eased in nice and gently.
“He will be on the bench again at the weekend, he might get 15, 20 minutes if things are going well.
“But that is the only way he is going to get into the team, is by easing him in gently.
“Tonight, he looked a long way away from being able to play 90 minutes.“
Fraser has not played a single minute of league football since March; he declined to extend his Bournemouth contract beyond the summer.