Goals from Andriy Yarmolenko and Yevhen Seleznyov secured a two-goal advantage over their rivals in Lviv on Saturday, moving Ukraine a step closer to the finals in France next year.
However, Fomenko urged caution from his players and insisted only one half of the tie is finished, calling for focus ahead of Tuesday's return leg .
"We have won the first half of our tie, and I am delighted with the clean sheet, but now we should prepare for the second," he said. "Tuesday's game will be the final decisive one.
"After the first goal we made some mistakes, individual mistakes – maybe my players started to relax.
"It's a bit disappointing that we didn't get the third goal, but saying that we didn't concede either.
"Now we need to calm down. Our players know what they have to do in the second leg."
His Slovenia counterpart Srecko Katanec rued a lacklustre display in front of goal from his side, but retained some hope they can turn the tie around next week.
He said: "It was very disappointing that we missed all our chances, particularly one at the start of the game.
"However, we still have the second leg so this is not the end of our campaign. We still have to play at home and our fate remains in our hands.
"We will try to produce our best football at home and will try to secure a result."