The 18-year-old said opening his senior account didn't matter as Falkirk chucked away a two goal lead to lose 3-2 against the Honest Men.
"It doesn't really count for anything. Fair enough I got a goal but it was a defeat so it doesn't really matter, to be honest."
Rudden handed the Bairns the advantage as his shot sneaked in at the near post after he was set up by Deimantas Petravicius.
And Petravicius made it 2-0, before Ayr came from behind to take all three points.
"It felt good at the time but everyone is hurting and I am hurting. It needs to be better. Being 2-0 up at half-time and then to lose three goals is not good enough."
Rudden, who was in the squad for the first time, believes that there is spirit in the dressing room, and that there is a sense that things are slowly improving.
"When we played Falkirk, when I was at Rangers, in the Irn-Bru Cup - we battered them but they were just experienced.
"There's a lot of spirit in the dressing room and we are all hurting at that result, but we will definitely come back from it."
Rudden is the newest of the 17 summer signings in the squad, having signed on deadline day - just after Ray McKinnon was announced as new manager.
The youngster added that he had no previous contact with the boss, and he is simply aiming to get minutes and impress Rangers boss Steven Gerrard.