Liverpool enjoyed the lion's share of possession against the Gunners but succumbed to two goals from Robin van Persie after a Laurent Koscielny own goal had handed the home side the advantage.
Having spurned numerous opportunities to put the game to bed Kuyt also missed from the penalty spot after Wojciech Szczesny had felled Luis Suarez, while the Dutchman also hit the post twice.
The Reds first defeat at Anfield this season left them ten points adrift of Arsenal, who occupy the fourth and final Champions League qualification spot, but Kuyt believes the wrong team walked away with all three points on Saturday.
“It's very disappointing. I thought the team played really well. We should have scored at least three goals,” Kuyt told the club’s official website.
“I enjoyed linking up with Luis Suarez and we created enough chances but we need to kill those chances.
“To lose was just unbelievable. Without Van Persie they are a completely different team.
“I had a feeling I didn't hit the penalty as properly as I normally do but that's football - sometimes you score goals, sometimes you miss penalties.
“We had other opportunities to kill the game."
Liverpool will once more be counting the cost of their wasteful nature in front of goal that cost them valuable points, with both Kuyt and Suarez both guilty of failing to find the back of the net when presented with the opportunity to do so.
The former Feyenoord forward will have the chance to make amends for his penalty miss as Liverpool embark on a crucial run of games, with a trip to the Stadium of Light coming before facing Everton in the Merseyside derby and Stoke in the F.A Cup.
"With no midweek match we now have some time to recover after a lot of games over the last few weeks," Kuyt continued. “We will be fresh for the Sunderland game."