The Brazilian scored two exceptional goals as West Ham came from behind to beat Southampton.
Manuel Pellegrini expects Felipe Anderson to go from strength to strength for West Ham in the second half of the Premier League campaign.
The Brazilian scored two stunning goals in the space of six second-half minutes to secure a 2-1 comeback victory for West Ham over struggling Southampton on Thursday.
Having started all 19 of his side's league games, Felipe Anderson now has eight goals to his name, and Pellegrini believes the former Lazio winger still has plenty of scope for improvement.
"I always say that Felipe is just knowing what it is to be playing in the Premier League," said the Chilean.
"In every game he is improving, it is not easy for a midfielder to score eight goals in the middle of the season, I am sure that he will continue improving in the second half."
15 - West Ham have won 15 points in the Premier League in December (P6 W5 D0 L1); their most in a single month of a season in competition history. Bubbling. pic.twitter.com/GYaarnYBsj— OptaJoe (@OptaJoe) December 27, 2018
However, Pellegrini is unsure if Felipe Anderson can be classed as the best player outside of the Premier League's top six clubs just yet.
"I don't know that," he added. "I think for me it is more important that the team plays well and that Felipe is playing well in that, in that you always need high individual performers to win."
Victory took the Hammers into the top half, having won five of their last six league outings, a remarkable turnaround after they lost their opening four games of the campaign.
But Pellegrini insists his men must take things game by game if they are to maintain their fine form.
"It depends if we keep playing in this way," he said.
"I said during the week that we needed to recover those three points that we lost at home against Watford and if we are also able to get 27 points, it was a very good first half [of the season] for us."
The Saints, meanwhile, remain just three points above the relegation zone, and boss Ralph Hasenhuttl was frustrated at how easily his side capitulated.
"The way we lost it was too easy, we didn't play such a good game," he told BBC Sport.
"If you give it away like we did then you don't deserve to win. [Their goals] were too easy."