Kuyt, who played more than 200 games for Liverpool between 2006 and 2012, was last week named interim coach of Fenerbahce while they search for a permanent manager following the resignation of Ismail Kartal.
Just two matches into the job, the Dutchman delivered Fenerbahce's first victory of their Champions League campaign, thanks to Vedat Muriqi's 79th-minute winner.
"I'm very happy with all the players, I'm very happy with all the people who were involved that we made a miracle tonight because I think not many people expected us to win (playing) Liverpool," Kuyt told reporters.
"But we said before the game to each other, 'we have a chance'... The win tonight was not an easy win, but it was not luck. At the end of the day we deserved it. We created many chances, we kept pushing and we keep fighting against one of the best teams in Europe.
"We are back in this competition. I think a lot of teams have to still play tonight, but we are now in a position which gives us the right to play in the playoffs. And I think we have a great chance to reach this stage."
Fenerbahce are 19th in the Champions League standings with five points from four matches.