The green Jersey holder edged Alexander Kristoff to the line in an exciting sprint photo finish at the end of a long 209km journey from Moirans-en-Montagne to the Swiss capital of Bern. "I think most people in the peloton are scared of him and his ability".
Slovak Sagan claimed his third victory of this year's Tour and seventh in total with the third photo finish of the current race, clocking 4hr 26min 2sec.
"I don't agree [with the headline]", said Froome.
Germany's Tony Martin and France's Julian Alaphilippe lit up the early stages of the 209 kilometre route from Moirans-en-Montagne to Bern, with the duo tagging an ambitious breakaway after 13 kilometres.
Sagan also won the world title with a late breakaway in the USA a year ago.
Martin, a three-time world time trial champion, has established a reputation for long distance efforts in the past and the 31-year-old Etixx-Quick Step rider and his team-mate aimed to upset the favourites for the stage, which presented a final chance for sprinters ahead of Paris.
"It was a very hot stage", Sagan told ITV4 after his latest triumph.
Froome kept his 1-minute, 47-second lead over Dutch rider Bauke Mollema, with Britain's Adam Yates in third, 2:45 back.
"Other teams have said they're going to attack this week in the Alps and I expect they will", he said.
The final day of the Tour of Poland went ahead as planned, after yesterday's stage was cancelled due to adverse weather conditions.
"The main thing for me and for Team Sky [today] was just to get me to the finish in one piece, hopefully not taking any gaps to my rivals or anything like that", Froome said. "All you need is one bad day in the mountains and you can lose minutes".
There was a minute of silence at the start of the stage to pay tribute to the 84 victims of the truck attack in Nice.
The peloton crossed into Switzerland midway through the leg, riding through lush, green valleys with views of snow-capped mountains before crossing through the medieval center of Bern, which is a UNESCO World Heritage site.
Britain's Chris Froome seems to be heading for a third Tour de France title seemingly unchallenged as rivals fail to unsettle his well-oiled Team Sky machine but try telling him that.
That provoked a counter-attack from former world champion Rui Costa of Portugal, but he was caught 4.5km from the finish, and thereafter it was all about Sagan and Kristoff.