Zlatko Dedic scored the game's only goal to put Slovenia through on away goals at the expense of Guus Hiddink's side, who had two men sent off in a dramatic and bad-tempered match. But Kek was in no doubt that his side performed better on the night and deserved to go through.
He said: "It was a historic match for us. I want to thank every one of my players. The whole country was behind us and we could feel their support. Our victory was deserved. It is a huge honour to be among the best teams in the world. Slovenia has realised a dream.
"Today's victory is not down to any individual player, but the team as a whole. We prepared thoroughly for this match and analysed the Russian style of play beforehand. I'm so pleased that we accomplished our plan."
Disappointed Russia coach Guus Hiddink highlighted the 66th-minute sending off of Aleksandr Kerzhakov as the game's turning-point. "We are very disappointed with the outcome, and the players have not hidden their disappointment in the dressing room," he said.
"Alas, the reality is that Russia will not be going to the World Cup finals. The key moment was Kerzhakov's sending off, plus the goal we conceded in the first leg.
Hiddink was nonetheless dignified in defeat, paying tribute to Slovenia's never-say-die approach, saying: "You have to give them credit. They fought to the end for this chance. The goal at the end of the game at the Luzhniki gave them hope, and today they used their advantage at on their home ground."