Ralph Hasenhuttl called for unity after Jannik Vestergaard's "terrible mistake" consigned struggling Southampton to a costly 1-0 loss at Cardiff City.
Danish centre-back Vestergaard gifted Callum Paterson the only goal in the 74th minute with a poor backpass amid dreary conditions.
The error came just as Southampton had begun to find a foothold in the match and left ex-RB Leipzig coach Hasenhuttl - appointed as Mark Hughes' successor on Wednesday - with plenty to ponder.
His team are three points adrift of safety and grappling with an 11-match winless streak in the Premier League, but the Austrian is eager for his players not to turn on each other.
"In the second period our performance was better and better," Hasenhuttl said in quotes reported by the BBC.
"We had a few chances but in this best period we nearly made an own goal. It was a terrible mistake.
"The mentality was okay. We never gave up. I have seen some good things from my team but we made too many mistakes.
"We know that we have a hard and long way ahead of us. There are guys in the changing room with their heads down.
"It's all about staying together and taking the next step in our development."
FULL-TIME Cardiff 1-0 SouthamptonA frustrating first match for Ralph Hasenhuttl as his Southampton side fall to a Callum Paterson finishDecember 8, 2018
Cardiff, in contrast to their relegation rivals, are now up to 14th courtesy of four wins in their past five home fixtures.
Neil Warnock believes the upturn in results is the sign of a team becoming increasingly comfortable in the Premier League.
"I thought we deserved it. We missed three or four good chances," the Bluebirds boss told BBC 5 Live Sport.
"Paterson works hard and I thought all the way through we created better chances, and we played better football.
"We've improved nearly weekly. We play a lot more than people give us credit, but we don't kid ourselves. We've got a long, hard winter ahead of us."
