Ter Stegen lamented his "unlucky" error at the WWK Arena in Augsburg, that was not helped by the conditions.
A volley from Juraj Kucka bounced twice on the wet pitch in front of half-time substitute Ter Stegen, and Manuel Neuer's understudy saw the ball trickle through his legs and into the net.
"It was an unlucky situation, of course," the Barcelona goalkeeper said.
"The ball bounced two times and I didn't see it anymore because of the water.
"For sure, it's my failure. No question."
Earlier, veteran striker Mario Gomez put Germany ahead from the penalty spot late in the first half.
Napoli's Marek Hamsik scored a brilliant equaliser in the 41st minute before Michal Duris put the visitors in front, but the costly error came for Slovakia's third goal in the 52nd minute.
Germany face Hungary on the weekend in their final warm-up game for EURO 2016, where they face Ukraine, Poland and Northern Ireland in Group C.
