The Hammers are currently sixth in the table, just six points outside the top four.
The Hammers currently sit sixth in the table, just four points away from Tottenham Hotspur in fourth place, after a fine first season under Slaven Bilic.
That means they are very much in the race for a Champions League place, with the open nature of the league meaning they and several other sides have every chance of qualifying for Europe this season.
And Payet says they must be ambitious and consistent to finish at the top end of the table.
“We have to be consistent if we want to finish toward the top of the table,” he told whufc.com.
“We have to be ambitious. We know there are some big teams above us but it’s up to us to continue as we played on Saturday, to put our game in place.”
“The battle’s going to be tough, but we mustn’t get carried away, we have to stay concentrated.”
If West Ham are to finish as high up the table as possible, Payet will surely be key to their hopes of doing so.
The Frenchman has very much been the star man in Slaven Bilic’s side this season, with a series of impressive performances having been key to their impressive firs season under the Croatian.
With him now back fully fit from his long injury lay off, they will be hoping he can continue to star and help them to secure a place in Europe next season at the least.