Goals from former Swansea midfielder Andrea Orlandi and Jose Ulloa condemned Cardiff to just their second home defeat of the season and boosted Brighton's play-off plans.
But Malky Mackay was left wondering how his side failed to make the most of a host of chances as they were denied four times by the woodwork and by the superb Kuszczak.
Oatway said: "We were fortunate to get him as I think he is a Premier League player and he is one of the best keepers outside of it.
"Hopefully he keeps giving us performances like that. If you are going to achieve anything in this league - or any league - you need a good goalkeeper."
But Oatway does not believe Brighton's hosts have any cause for concern as they look to get back on track against Wolverhampton Wanderers this weekend.
He said: "Everyone knows Cardiff have been up there all season and to get any points here is a great achievement.
"We knew they would throw everything at is but they boys were magnificent the way they about their business.
"I think Cardiff will be untouchable and they won't get caught so the boys are delighted to have won it."