The Hammers drew 1-1 with Everton in an entertaining clash at Upton Park on Saturday. Manuel Lanzini gave the hosts a lead midway through the first-half, before Romelu Lukaku equalised shortly after.
While there was plenty of quality on display from both teams and a draw remains a positive result, Bilic had more pressing matters on his mind after the game in relation to suspected further injuries.
Payet had to come off following a tough tackle from James McCarthy, while Valencia lasted just 19 minutes after coming on for only his second appearance since his lengthy layoff.
“We lost Payet because of a bad tackle. We can only hope that he will be okay and it is not going to be long-term, but we have to wait for the scan,” Bilic told the BBC.
"Then Enner Valencia came on and was injured too. Until we get the scan, we don't know how bad it's going to be. We hope that both players will be okay for the Spurs game after the international break.
"But many times, I've been told it's going to be okay and then I get a call late at night, I speak to the physio and I learn it's going to be six to eight weeks. So we will see."
Bilic has not had the best of luck in terms of keeping his West Ham United squad fully fit since he was appointed as the club’s new manager over the summer.
Andy Carroll, Mauro Zarate, Valencia and now Payet are just four of a number of players who have picked up knocks, strains, pulls and other types of injuries.
The Croatian coach will be hopeful Payet will not be out for too long, what with the France international becoming such a key member of the first-team and one of the best talents in the league.
The former Marseille ace has five goals and a further three assists in 12 Premier League starts.