McGovern, who plays for Scottish club Hamilton Academical, made a string of saves to limit the damage at Parc des Princes, but Mario Gomez's 30th-minute strike was enough for Germany to reach the last 16 as Group C winners.
Having finished third in the group behind Poland, Northern Ireland now face an anxious wait to see if they will qualify as one of the four best third-place teams.
"If it is not meant to be for us to go through, we will be very disappointed," McGovern said.
"It was busy today and mentally very hard. We knew every goal was crucial so we wanted to keep it at one and maybe nick a goal of our own.
"Germany had a slow start, but they were excellent today. We could not get out."
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