Eustace’s side were beaten 2-1 by Saints, which made it six successive wins and 17 matches unbeaten in all competitions since mid-January.
Taylor Harwood-Bellis headed in the winner from a Ryan Manning free-kick, which was awarded for an Oscar Fraulo foul on Flynn Downes.
Tonda Eckert’s charges, who beat Arsenal in the FA Cup quarter-final last week before thrashing Wrexham 5-1 on Tuesday, are climbing the table.
Saints are up to fifth in the Championship, and dealt Derby – who are eighth and now five points off the play-offs – a potentially fatal promotion blow.
After the match, Eustace said: “In the first-half, I thought we were excellent. We took the game to them, pressed very high, and won the ball back.
Derby County manager John Eustace is an experienced Championship boss (Image: PA)
“We scored a great goal. In the second half, we knew we’d be under pressure. They scored a good first goal, but the second was just not acceptable.
“It’s really, really soft and something that I’m really disappointed about. We needed to shuffle across to defend the set-piece, the whole group.
“You know, it’s something we worked very hard on, for and against. We scored a great goal from a set-piece, which was worked on yesterday.
“But then we conceded one on which the whole team wasn’t doing their jobs. I don’t think it was a free-kick either,” he concluded.
Asked if he feels the result was down to Saints simply showing their quality, Eustace added: “No, not at all. They scored a second goal really cheaply.
“We needed to be better in the final third. First half, we were excellent. But they’re on a good run, and we’ve given them the second goal today.
“We lost our left-back to injury yesterday, we lost Bobby Clark, we lost Patrick Agyemang, and Rhian Brewster. There are lots of top players we haven’t got.
“But the effort the boys put in today against the fantastic squad of players. Their quality is a different class. Yeah, of course it is.
“But what an effort from my players. They’ve done it all season. The most disappointing thing is that the second goal just wasn’t good enough.
“Southampton have got top quality in every position, and they’ve probably underachieved up to now to where they are. I’m sure they’ll keep growing.
“They will keep building and, you know, they’ll be certainly strong contenders for the promotion. And so they should with the squad they’ve got.”