The Slovenians appeared to be heading for a berth in the last 16 after goals by Valter Birsa and Zlatan Ljubijankic gave them a 2-0 lead in the first period but ran out of steam and lost concentration under fierce U.S. pressure in the second.
"We played a fantastic first half but the goal we conceded straight after the break rattled us and we never recovered from it," Kek told a news conference after the pulsating clash.
"It was a lapse in concentration after which we lost our focus and allowed them back into the match."
"We are not thinking about the last group game against England right now because we have to recover physically and mentally from a tough battle."
MENTAL BLOCK
Slovenia right-back Miso Brecko added: "We are very disappointed because we had a great chance to secure a berth in the knockout stage and we didn't because we weren't aggressive enough in the second half."
"It was like we had a mental block after the interval, we got only a point from a match we should have won and we have to live with it now.
"It wasn't our intention to sit back on a 2-0 lead but, wishing to hold on to that precious advantage, we dropped back far too much and allowed them to pin us into our own half."
The U.S. had a goal controversially disallowed in the closing stages after they equalised and Slovenia centre back Bostjan Cesar conceded they were lucky to avoid defeat.
"I didn't see the foul but we are glad the goal didn't stand and in the end we were a bit fortunate to get a draw, having spilled a two-goal lead," he said.
"But the referee also tolerated some rough tackling from the United States right from the kick off so we can also complain.
"Passage to the last 16 is still in our hands. England will start as the favourites against us but they are a playable team, we can stand our ground against them."
England play Slovenia in Port Elizabeth next Wednesday.
