Ellis Genge took a swipe at the "sausages" who criticised England following a Six Nations defeat to France after they beat Scotland to regain the Calcutta Cup on a bleak Saturday at Murrayfield.
The Rugby World Cup runners-up made a poor start to the tournament last weekend, paying the price for an error-strewn performance by losing 24-17 in Paris.
England rolled up their sleeves to respond with a 13-6 victory in a Storm Ciara-battered Edinburgh, Genge scoring the only try 10 minutes from time.
Jones' side showed they were up for the fight in driving rain and strong winds and the replacement prop let his feelings be known after they lifted the Calcutta Cup for the first time in three years.
Asked about the emotion of scoring the winning try, he told BBC Sport: "I don't know; I can't remember. It was 20 minutes ago, and it was all a bit of a blur, it happens quite quick.
"We played well and luckily I was the one that picked it up. Quite a few of the boys are getting drug tested so it's quite quiet in the changing room.
"We are buzzing to win but there is more to come. We had a bump in the road last week and people were saying we were not good enough.
"It's classic – you have a lot of sausages that say things that come to their head. What are they on about? We go away and win in Scotland in the rain and they are full of praise again. I hope we have shut them up."
Jones is hopeful his side can kick on with a showdown against Ireland to come at Twickenham following a weekend off.
"Apart from 15 minutes, we dominated the game. We had a few poor kicks, but we dominated possession and we finished it off, which we didn't do last week," said the England head coach.
"It was an old-fashioned Calcutta Cup game, swirling wind and an aggressive crowd without manners.
"There is a lot of growth for us. I under-prepared the side for the first game but we'll get stronger as the weeks go on."