The 21-year-old will lead the line for United this season following Romelu Lukaku‘s departure.
After scoring twice against Chelsea on Sunday, Rashford has proven he can be the main man at Old Trafford.
“There are big expectations on Marcus and I thought he put his penalty away clinically and I look at him as a more instinctive finisher,” Pallister said.
“Sometimes he has too much time, but I thought on Sunday he was clinical as he had a little bit of time but he put his second away fantastically well. Maybe that’s something that Ole has been working on with him, as there was no better finisher than Ole Gunnar.
“When you get into those situations you want someone with a cool head and immaculate finishing, and Marcus was absolutely clinical with his second goal.
“There’s been a lot of expectation on Marcus for both England and Manchester United for a while. He will play in a three-pronged attack either up front or on the flank, and he’s comfortable in all of those areas. He’s maturing, and there’s no doubt he’s the man now Lukaku has gone.”