Kek's men are now unbeaten in nine games and qualified for the knockout stage as one of the best third-placed teams after drawing all of their Group C matches.
Slovenia only missed out on second place in the section due to Denmark's superior disciplinary record.
"I didn't expect to be going into the knockout phase," said Kek. "But we showed with our play we deserved to be here and go into the knockouts against one of the favourites for the tournaments."
England were booed off in Cologne despite topping the group after creating precious little.
The Three Lions' best chance came in stoppage time when Jan Oblak saved Cole Palmer's strike.
Slovenia had conceded with virtually the last touch of the game in their previous match against Serbia and Kek was grateful to avoid the same fate.
"It was the 90th minute when the English team had a big opportunity, but Jan hasn't had that much work," added Kek.
"This was a kiss of fate and we were lucky. The luck we lacked against Serbia we had today."
Slovenia will have to wait until Wednesday's final group games are completed to find out who they will face in the last 16.
