The tone for the second Test was set on the opening morning, when South Africa elected to bat first under gloomy skies at Emirates Old Trafford, only to be skittled for a paltry 151.
England went on to wrap up an innings-and-85-run win inside three days, with only Keegan Petersen and Rassie van der Dussen showing resistance for the Proteas, who were all out for 179 in their second dig.
While Elgar has called for more output from his batters, the South Africa captain insisted they will regroup quickly before the series decider at the Kia Oval in a fortnight's time.
"The bottom line is we need runs from the middle order, and at the moment that is letting us down quite a bit," Elgar said. "As much as guys don't want to hear it, I think they know that already.
"I don't want to treat a guy like a schoolkid, that's definitely not my way because I wouldn't have liked that when I was a younger player, but we'll definitely have a few chats going forward.
"Sometimes you can go into panic mode when things like this happen. Myself and the coach (Mark Boucher) are definitely not those kinds of guys to panic. We know we're still a good side.
"Let's not forget why we're here. We're here to win a Test series and we're in a great position to still a win a Test series. We'll clear our minds, let the dust settle and focus on the third Test."