England have been drawn in a group alongside the two minnows and Australia, with whom they are much more familiar having done battle regularly in the IRB World Series.
However, despite being heavy favourites to comfortably beat both Sri Lanka and Uganda, Amor is wary of the danger posed by the smaller nations.
"The standard at the bottom has really come up. The honest truth is we don't really know until we get there, but in the Sevens environment you cannot think about day two, you cannot think about the next game, you have to focus on your first game because it is all about building momentum," Amor told reporters.
"There are too many good teams out there that are currently smaller nations that could quite easily turn you over. Our focus is very much getting Sri Lanka right first and foremost, and then building from that moment to do Uganda and then Australia."
England, who will play all three of the group games on July 26 at Ibrox Stadium, revealed their 12-man squad for the Games earlier today.