Fenerbahce lost 2-1 at home to Goztepe to make it a run of just one win in five games across all competitions. The Istanbul giants opened the week with a four-week deficit to league leaders Galatasaray, but saw the gap grow to 10 points after Monday's derby defeat and Saturday's loss.
"We want to apologise to our fans because they deserve much more," Kuyt said after his first game in charge. "But at the same time, the fans also know the situation we are in."
Manager Ismail Kartal resigned after Monday's 2-1 loss to Galatasaray, putting Kuyt in charge until the November international break.
"We tried to bring good energy back into training. We believed we could get a good result today, but it is very clear to see that we can be very fragile at times," Kuyt continued.
Fenerbahce headed into the break with a 1-0 lead after Matteo Guendouzi put the hosts in front of the cusp of half-time, but two goals in the last 15 minutes earned Goztepe a famous away win at Sukru Saracuoglu Stadium - just their third in 56 years.
"In the first half, we had more than 72% possession, which is what we want; this is how we want to play, and we scored a nice goal. Afterwards, we wanted to do even more; we wanted to keep it up, but we didn't make a good start to the second half," Kuyt explained.
"Following that, we conceded a goal from an individual error during our build-up play. Since building up from the back is something I want, these kinds of individual errors might fall on my responsibility. But after that, we had three very clear chances: Kerem (Akturkoglu) had a header, Lukaku had a chance, and Kerem also had a shot that hit the post.
"If we had scored one of those, it would have been 2-1. Of course, in times like these, you also need luck on your side, especially given the situation we're in."
Reunion with old flame
Fenerbahce have now won just five of their ten Super Lig games and need to improve fast: Dirk Kuyt's next game as Fenerbahce head coach will be against his former club, Liverpool, in the UEFA Champions League.
The Dutch boss acknowledged that Fenerbahce are in a deep hole ahead of a momentous game against the Reds.
"We are in a tough situation right now, and to get out of it, we need to perform much better and do things better. It was a tough match; we certainly did our absolute best to win today, but unfortunately, we couldn't get the result we wanted, so we are feeling major disappointment. We could have performed much better."
