Both clubs entered the match in the bottom three but it was Fulham who climbed to 16th place with a 2-1 victory at Craven Cottage.
It was a critical result for Rene Meulensteen's side after they were embarrassed 6-0 by Hull last Saturday in a performance that prompted several players to issue apologies to fans.
"After Hull it was important that you give the right answer and we did that in a six-pointer against West Ham," Riether said.
"The result against Hull was not good, we wanted to get some points.
"We were in the changing room after that performance and we didn't know what had happened.
"When something like that happens it's important you forget it as soon as possible because at the moment every few days you have a match.
"The manager found the right words and you saw the response on the pitch."
The drubbing at Hull was the only setback in an otherwise successful Christmas that yielded six points in three games, all against relegation rivals after Norwich were also dispatched 2-1 on Boxing Day.
The campaign is interrupted by Saturday's return to Carrow Road in the third round of the FA Cup, before Premier League action resumes against Sunderland at Craven Cottage a week later.
"Sunderland at home will be a very important game as well and that's when we need to take the next step," Riether said.
"We got the three points against West Ham, but just as importantly was that we created a lot of chances and applied a lot of pressure."
Meulensteen took the gamble of playing Dimitar Berbatov and Adel Taarabt in tandem against West Ham after the gifted, if unpredictable, duo were passed fit from respective groin and ankle injuries.
Meulensteen felt the decision was justified by Berbatov's second-half winner.
"Dimitar knows how important this win was and we're delighted that both he and Adel were able to start because both were late shouts again," Meulensteen said.
"We weren't able to take the risks in earlier games and maybe credit to all of us for having that patience because it paid off for waiting that long because he got us the winner."
Problems are mounting for West Ham boss Sam Allardyce, who is under pressure as the club continue their battle with relegation.
Apart from having to contend with a lengthy injury list that still includes England striker Andy Carroll, the Hammers must face Manchester City, Chelsea and Newcastle in the Premier League this month.
"We've had four injuries in this period and it's catching up with everybody," Allardyce said.
"It's a great Christmas period that everyone likes, but the cost is massive to each and every football club across the country.
"We're losing millions and millions of pounds of talent to injury.
"You expect at this time of year the odd suspension, but when you've got eight out, it ain't my fault.
"I'll use the players I've got to get the best out of the team."