The Poland international hesitated inexplicably upon receiving a routine backpass from Nathanial Clyne and his terrible attempts to turn Olivier Giroud resulted in the Arsenal striker opening the scoring at the Emirates Stadium on Saturday.
Southampton acquitted themselves well despite the setback but another needless error - Jose Fonte's pull on Per Mertesacker inside the box that allowed Giroud to dispatch his second - sealed their fate and Pochettino wants his high-flying side to eradicate such lapses of concentration.
"It's not really necessary to analyse what happened, we all saw it on the pitch," he told BBC Sport.
"We want to support our keeper in spite of this mistake - these things can happen in football and we need to work hard to make sure they don't happen again.
"I'm clearly unhappy with the result and the way we lost as well, but this is football - these things happen."
Southampton have done well against other top sides in the Premier League this season, having drawn at Manchester United and beaten Liverpool at Anfield.
Despite not being able to match those results against Arsene Wenger's side, Pochettino was satisfied with the overall performance of his team.
He added: "We competed well though, in Arsenal's ground - the league leaders.
"We competed until the last minute and that's the positive. We tried our best."
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