Key to Scotland win over France was fast start, says Steyn
The 32-year-old was named man of the match after he and fellow wing Darcy Graham scored two tries each in a match they actually led 47-14 at one point.
That would have been a record Scottish victory over France but instead Steyn and his teammates had to settle for a highest ever score after outscoring France by seven tries to six.
"I think we knew you couldn't come and try to contain them, you had to fire shots at them," Steyn told the BBC.
"You just knew it was going to be a great day.
"It was all about making sure we fired the first shot.
"I was more worried about how much we were celebrating, we needed to get our feet on the ground and keep going."
Despite their chastening afternoon, France earned a try-bonus point that kept them on top of the table with a huge points difference advantage over Scotland ahead of the final round of matches next Saturday.
Scotland travel to Ireland, who can also still win the title, with France hosting England.
France and Scotland both have 16 points to Ireland's 14.
French lock Charles Ollivon bemoaned his team's ill discipline.
"It just got away from us. A lot of indiscipline, not enough commitment," he told French channel TF1.
"Now it's done, it's behind us. We have to be able to switch back on this coming week. We have to get over it and start again from a solid base to go after the title next week."
To that end, the bonus point was crucial.
"That was the aim, to score four tries," he added. "We managed to do that in the second half to keep our destiny in our own hands."