The Arsenal playmaker received some criticism for a string of below-par displays in the second half of the campaign after joining the Gunners from Real Madrid last summer.
And Rangnick feels that the Germany international desperately needs to improve his work off the ball – along with the rest of his Arsenal team-mates.
“Mesut has tactically not really evolved over the past two years,” Rangnick told Frankfurt Allgemaine.
“The fact that he is a gifted footballer, everyone knows that. But in the game against the ball he still has major weaknesses.
“I have in the past season seen some games of Arsenal. They often conceded too many goals in big matches, because no work was done after losing the ball enough, to win it back.
“With Mesut it is a temperament problem. If he had played in the past two years at Dortmund or Bayern, he would be tactically much better.”
The 25-year-old, who is on international duty with Germany at the World Cup, scored five goals and made nine assists in 26 Premier League games last term.
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