England head Group H on goal difference but victory for Ukraine in Kiev would take them two points above Roy Hodgson's men at the top, with only two games to play.
Fomenko has led Ukraine to four straight qualifying victories since taking up his role in December, securing away wins over Poland and Ukraine, as well as a 9-0 demolition of San Marino on Friday.
Asked if Tuesday's game was the biggest match of his life, he replied: "Not only of mine.
"Because with victory, this match gives us the possibility to achieve our objectives.
"We don't want to make you (the Ukrainian people) angry."
England needed an 87th-minute penalty from Frank Lampard to salvage a 1-1 draw when the sides met at Wembley a year ago, but a poker-faced Fomenko shrugged off talk of previous meetings.
"There have been some changes in the squads," he added. "There are changes in the Ukraine team and the England team. We will only know the answer to this precise question on Tuesday."
The tight-lipped coach, whose side has conceded only four goals in qualifying, also stayed coy on his plans to counteract a less familiar face up front.
Asked what he knew about Rickie Lambert, the Southampton target man due to lead the line in the absence of Wayne Rooney, Daniel Sturridge, Danny Welbeck and Andy Carroll, he replied: "It's a secret."