All of the action came in the first half as Issy Moore's equaliser in the ninth minute cancelled out Elliana Martin's opening goal. It was her second goal that settled the tie with Brighton's goalkeepers Silvana Marshall-Miranda and Sian Woods making a flurry of excellent stops throughout.
In the end, City were unable to break down their defensive resolve as Cook admitted their lack of ruthlessness in front of goal proved costly.
"A frustrating one, I think," Cook reflected. "One where they've had two opportunities, scored two. We need to score one of the eight opportunities. Full credit to Brighton's two keepers, one that was brought one on, because both of them were fantastic.
"Ceri's had a header in the last five minutes there, where their keeper pushed it onto the bar. Another day, they go in and it's the same with several of our other chances. We've created good chances, and that's frustrating because we didn't finish them. Full credit to Brighton, and I hope they do well now.
"The games that we've watched, the reports that we got of them, everything that we've seen of Brighton, we didn't expect that of them. Full credit to them because they've come into a knockout competition and they haven't tried to play.
"They've gone longer from short goal kicks, they've then gone longer. They haven't done the usual PGA (pro game academies) work. It's a part of the game, it's the dark arts, and we need to get better at it across the whole of the game."
Action of Norwich City Women during their FAWNL Plate defeat to Brighton U21s. _(Image: Matt Usher/Norwich City FC)_
There was more concern for City on the injury front after striker Tash Snelling and Grace Riglar limped out of the contest in the second half.
Cook is confident those issues will prove to be minor, but it graphically illustrates the thinness within the squad at present after a string of injuries that have seen City lose a host of front-line options in recent months.
"Hopefully, they are just knocks. I've said to them in the huddle, they can all have tomorrow night off now because it's one where we're all knackered," Cook admitted to City's channels. "They're tired, we've got no numbers, we've got a bit of an injury crisis as well, and so we just need to make sure that we're chilling out.
"So we're going to rest minds, rest bodies and injured players can come in and see Robin. We'll get in the pool and make sure we're sorted from that point of view. But we're not going to be in tomorrow night and working on the pitch or anything like that."
That additional period of rest is something City's boss will hope to re-energise his squad ahead of their trip to Chatham Town next Sunday.
"If anything, it's about leaving this game. It's leaving this game where it is because Chatham are a very good side," said Cook. "We've been working on a game plan for them for a few weeks as staff and now we can make sure that the players are ready for that.
Action of Norwich City Women against Brighton U21s at the Nest on Sunday. _(Image: Matt Usher/Norwich City FC)_
"The thing for me is freshness. I want fresh minds and fresh bodies for Tuesday and Thursday night to ensure we're ready for the week.
"We're in a beautiful position in the sense that we can now start the week properly from Tuesday. We can relax our minds and our bodies. It's all part of the plan for what we want.
"I think one of the other things as well, when you give people an evening off like that, they give you a little bit more because everybody loves a nice little evening. They can enjoy themselves and if they do come in they can sit in the pool and recover.
"If they have the evening off, hopefully they'll watch something nice on Netflix or anything else that's available for them to watch."