The France international scored United’s equaliser in a 1-1 draw with CSKA Moscow in the Champions League on Wednesday night.
You’ve got to be really careful when you throw all these accolades at young players
The 19-year-old striker has scored five goals in nine games in all competitions following his £36m move to Old Trafford on transfer deadline day.
Former United centre-half Pallister is concerned that Martial could suffer the same fate as Adnan Januzaj, who moved to Borussia Dortmund on loan in the summer.
“It’s really exciting to see a young player come into the team and have an immediate impact,” Pallister told Goal.com.
“But we saw that a couple of seasons ago with Januzaj, where we all went on about him being the new Ryan Giggs or the next Georgie Best.
“In the early part of his career he took Manchester United by storm, but he’s flat-lined since then. So you’ve got to be really careful when you throw all these accolades at young players.”
Martial became Europe’s most-expensive teenager following his £36m switch to United from Ligue 1 outfit Monaco and the fee could rise to £56m.
The French youngster has scored against Liverpool, Ipswich Town, Southampton and CSKA Moscow across three different competitions this term.
The Red Devils forward could line up against Manchester City in the derby at Old Trafford on Sunday evening.
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