Greece head into Tuesday's final Group C contest with hopes of reaching the last 16, despite failing to find the net in their opening two games in Brazil.
A 3-0 loss to Colombia was followed by a spirited goalless draw versus Japan, a result that hardly seemed likely when captain Konstantinos Katsouranis was sent off in the opening period.
To have hopes of qualifying, though, striker Mitroglou knows that Greece must rediscover the Midas touch in front of goal, with only a win good enough.
"With the hard work we've been putting in and a little luck, the goals will come," he said.
The Fulham man is aware that Greece face an uphill task in the quest for victory, though.
"They have excellent players like (Didier) Drogba and (Yaya) Toure. But we have to look at what we are doing," added Mitroglou.
"The task is simple. We have to win."
