"He must understand the Premier League is difficult if you keep the ball at your feet," Pellegrini told Sky Sports.
"He is a different player, a player that in every game makes important plays... he loses too many balls; he will continue improving."
Anderson joined West Ham for a reported 36 million pounds from Lazio in the close season but struggled to make an immediate impact, scoring once in 10 league games.
However, he has emerged as West Ham's top scorer with eight league goals so far, including seven in his last nine appearances.
"His run of goals is important for him and the team," Pellegrini added.
"It's not easy for a midfield player to score so many goals by this stage of the season. He can change the score of the game in any moment."
West Ham have won five out their six matches in December to climb to ninth in the table on 27 points from 19 games. They travel to Burnley on Sunday.
(Reporting by Rohith Nair in Bengaluru; Editing by John O'Brien)
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