The holders remain top of the RBS 6 Nations Championship table from France on points difference, although hosts Scotland showed a vast improvement from last week's display against Wales in Cardiff.
Lewsey told BBC television: "We never thought it was going to be easy coming up here.
"The atmosphere at Murrayfield today was superb - very intimidating - and we knew that we would come up against it.
"Everyone had written Scotland off, but they are very brave and very passionate. They came out with all guns blazing, so credit has to go to them.
"It was a dogged game. It was not pretty, but we got the result we came to do."
On his own try, Lewsey said: "We have worked very hard on putting the pressure on the kickers, and luckily I got my hands to the ball."