Goals from Leo Scienza and Taylor Harwood-Bellis cancelled out Carlton Morris’ first-half header to give Saints their sixth win a row and extend their unbeaten run to 17 games.
Boss Eckert said: “It was an outstanding performance, I think the best one of the week. The boys have been absolutely outstanding today.
“We’re clearly on top in the first half, then we didn’t really finish our attacks to put it in the back of the net. You just have one loose ball and have to defend one corner, go down 1-0 and you don’t really know why.
“That’s just the way football games go sometimes and then to have that belief and just that deep, deep belief to keep going and being sure that the game then falls on to you.”
Derby led when Morris scored at the far post from Joe Ward’s corner but they were forced to defend wave after wave of Southampton attack.
Scienza scored a superb equaliser as he curled beautifully into the far corner to round off a swift counter-attack created by Caspar Jander and Finn Azaz.
Then, in the 69th minute, Harwood-Bellis connected perfectly with Ryan Manning’s free-kick to give Saints three points which saw them end the day in fifth.
It was Harwood-Bellis’ sixth goal of the season and Eckert believes the former Manchester City defender, who captained the side in their FA Cup quarter-final win against Arsenal, is showing more maturity each week.
Eckert said: “It’s very nice to see him growing because I think that he’s only getting better week by week.
“I think that he’s a completely different player to what he was at the beginning of the season and we’ll do everything to support him to continue on that development.”
The defeat leaves Derby five points off the top six with four games remaining but boss John Eustace says his squad should be proud of what they have achieved, stressing there is plenty left to play for.
Eustace said: “That first 10 games for me was the key. We obviously recruited a little bit late. We recruited players that were injured and then had to get up to speed, which they have done.
“The first 10 games was always going to be a really difficult ask. After that, I said we’d progress and we’d get better. We’ve done that. It’s been a fantastic effort. The season’s not over and we’re going to go again next week.”