Cardiff were relegated from the Premier League after a 3-2 home defeat by Crystal Palace.
The Bluebirds had to win to stand any realistic chance of catching Brighton, who play at Arsenal on Sunday.
Wilfried Zaha, who had a short loan spell at the Welsh club from Manchester United, put the Eagles in ahead with a low finish in the 28th minute.
Cardiff were handed a lifeline three minutes later when Palace defender Martin Kelly sliced the ball into his own net.
Michy Batshuayi restored the visitors' lead in the 39th minute and Andros Townsend added a fine individual effort with 20 minutes left.
Bobby Reid scored a consolation for Cardiff in the 90th minute - but it was too little, too late.
"They were better than us up front today. We had some great chances and it's been like that most of the season," Cardiff boss Warnock told BT Sport.
"We haven't had the rub of the green really second half of the season."
Cardiff's fans were chanting Warnock's name at the final whistle and he added: "You've heard this lot, haven't you? Fantastic.
"Unbelievable. They've been fabulous all season for me. I'm right proud of them and I'm proud of the lads as well.
"They've tried hard. We've shown limitations today and that's why we are where we are.
"But the club's arrived again now. It's alive and kicking and that's the main thing. When we first came here it was almost gone.
"I'm really proud of what we've done. It could have been a little bit closer, but things were out of hand."