Payet and Valencia were both injured during West Ham’s last match against Everton, after some hefty challenges were put in on them.
And Cresswell has bemoaned his teammates’ luck, admitting that it will be a challenge for the Hammers to cope without them both.
“We have all seen that tackle and it wasn’t the best on Dimi,” Cresswell said.
“Also Enner has had no luck this season. He did it early on in the season and now he has done the same again in the Everton game. But there is nothing you can do about that. You just have to get your head down to get fit again and come back even stronger.
“It is not easy as a player to see one of your fellow pros get injured and be out for some time, but we have to get on with our jobs and be as professional as we can, in training and on Sunday at Tottenham.”
West Ham had welcomed the return of Valencia prior to his latest set-back, and it will be frustrating for them to have to be without the Ecuadorian again.
Arguably, though, the loss of Payet will have a bigger impact on the team, as the Frenchman has been so pivotal this season.
Payet has been brilliant for the Hammers since signing during the summer transfer window, and he has already become his side’s talisman.
West Ham will have to prove that they can cope without the attacking midfielder in the coming weeks, and they are in for a tough test when they do return to action – with Tottenham Hotspur next up on their Premier League schedule.