The Chiefs halted a three-match losing streak in emphatic fashion, thrashing the Redskins 45-10 to earn their 10th win of the season having made a perfect 9-0 start.
Reid admitted that the three defeats on the bounce had been tough for his side to take, but he was delighted with how they responded against the Redskins.
"It's tough to lose three games in the National Football League, three consecutive games," Reid told The AP.
"It seems like a year, those are dog years as you would say - each week that you have a loss in the NFL. For the guys to come back and rebound after that, I was proud of that."
Reid also took the opportunity to pass on his congratulations to Sporting Kansas City, who won the MLS Cup on Saturday, as well as paying tribute to former South African president Nelson Mandela, who died last week.
"Sporting KC, I'm telling you it's hard to be a champion right? And they did it. I'm proud of those guys," added Reid.
"I didn't mention Nelson Mandela's death the other day, but what a tribute to mankind he is."
The Chiefs still sit second in the AFC West, one win behind the 11-2 Denver Broncos with three games remaining.