Riether turned 31 the morning after the thrashing at the Etihad Stadium, a result that nudged the Cottagers closer to relegation from the Barclays Premier League.
Instead of marking the occasion with an enjoyable Sunday, he was required to train along with his team-mates by disciplinarian boss Felix Magath.
"There was no big party, I had my family over and I invited the team over for dinner and that was it," he said.
"It's normal when you lose 5-0, you haven't got many reasons to celebrate. It wasn't such a big party."
Fulham prop up the Premier League, with Sunday's visit of Everton their next opportunity to bridge the four-point gap to safety.
Only seven matches remain but, critically, four of them are at home, with Norwich, Hull and Crystal Palace also due at Craven Cottage between now and May 11.
Riether is convinced they will secure a 14th season in the top flight by drawing inspiration from West Ham's recent climb up the table.
"There is a big belief because we have to play many teams around us," he said.
"We also have four points to make up, which isn't a lot if you win two in a row.
"When we played West Ham (winning 2-1 on January 1) people said they had problems, but then they won two or three in a row and now they are 11th.
"In football everything is possible as we have seven games. There are 21 points to play for, many matches to go.
"I'm not the person that says how many wins we need, I say we need to win the next game on Sunday. The next game is always the most important thing.
"It will be a tough one because Everton want to play in the Champions League, but we need to get points."