Petra Kvitova and Lucie Safarova claimed straight-set wins over Andrea Petkovic and Angelique Kerber respectively on Saturday.
It puts the Czechs just a win away from their third Fed Cup title in four years, and Rittner said the left-handed duo were simply too good on the opening day.
"It was [a tough day]," Rittner told the Fed Cup website.
"Obviously worst case for us being 0-2 down, but I have to say that the Czechs were the better players."
Kerber lost the first set against Safarova in unusual fashion, shouting 'come on' thinking she had hit a winner.
But Safarova returned the shot and Kerber conceded the point – and set – for hindrance.
"To me it was a pretty clear sign of losing the clearness of a point," Rittner said.
"You play a great point and usually she's really good at saying 'yes' or when she feels that this is a winner. She's really good at it. Sometimes I think 'wow, how did she know so early'.
"In this moment she didn't hit a winner, she thought she had hit a winner. Lucie got to it and she said 'come on' like as if the point was finished and for me it showed she wasn't really clear about everything that's going on."