The 26-year-old Belgian striker was sold to Inter Milan for £74 million on the last day of the Premier League transfer window after failing to make an appearance for United in their pre-season games.
The forward had fallen out of favour with Solskjaer at the end of last season as the Norwegian favoured Jesse Lingard, Marcus Rashford and Anthony Martial as his front three.
United signed Daniel James from Swansea City in the summer, another player with pace, and he scored the final goal of a 4-0 win over Chelsea on Sunday, with Rashford and Martial also scoring.
Pallister believes that Lukaku's weight counted against him.
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"I think Lukaku is a goalscorer and he will score plenty of goals, but the way they want to play at times, he’s too heavy," Pallister said, speaking to AmericanGambler.com .
"You look at the pace in the present game; maybe Ole is looking at that and saying he can’t implement that into his game for me. He was surplus to requirements.
"He’s a goal scorer, an instinctive goal scorer. He’s not the most clinical but he will get you 15-20 goals a season, but we were looking for a more rounded player.
"He plays Lingard, Martial and Rashford, and we caught Chelsea napping on the ball high up the pitch. So when you can do that you’ll have more space to go into and score more goals."
The former United defender suggested that Mason Greenwood is in line to feature in attack with an emphasis on speed,
"I think they have Greenwood coming through, and he looks a special talent," he said.
"You don’t like to get ahead of yourself with kids of that age, but it’s been a while since I’ve seen anyone be that comfortable in that environment at that age.
"He’s six foot odd, can use both left and right feet, knows how to score a goal and he looks the real deal at the moment. He’s still got a lot of work to do, he has to mature and find his feet at that level.
"The fact that Ole has played him a lot in pre-season, and had him on the bench on the weekend suggests he’s ready for the Premier League."
United striker Alexis Sanchez could be another casualty of the shift towards younger and quicker players, though he his wages may prevent any move away before the European transfer window shuts.