Lampard will 'go again' after Everton crash amid fans protest
In a fresh sight of the turmoil enveloping Everton, the club's board of directors were ordered to stay away from Goodison Park this weekend due to perceived security risks.
The move came after offensive messages, including death threats to chairman Bill Kenwright, were made to specific individuals during the week.
Everton officials called it a "profoundly sad day" and matters were no better on the pitch as Lampard's men squandered the lead given to them by Amadou Onana's first goal for the Toffees.
James Ward-Prowse scored twice as Southampton moved level on points with Everton, who are only off the bottom of the table on goal difference.
Everton have managed just one win in 11 league matches and have their joint-lowest tally (15) at the halfway stage of a Premier League campaign.
That wretched performance added extra numbers to the planned sit-in protest after the final whistle as fans called for owner Farhad Moshiri to sell up, with some also demanding Lampard's sacking.
The last time the Merseysiders had 15 points at this time of the season they were relegated in 1951, but Lampard is determined to keep fighting to save Everton, who narrowly avoided the drop under his leadership last term.
"It was a tense game, one that we lost. Frustrated to lose, frustrated for everyone," Lampard said.
"I don't know about forgetting how to win. It's clear in football that sometimes if you aren't winning games it can become contagious in terms of confidence and we know we are in that spot.
"Both of their goals could have been stopped from our point of view. It feels like a casual statement -'forgetting how to win' - but I understand the point - we are in a period of games where we are not winning."
The threats to Everton's directors came after chief executive Denise Barrett-Baxendale was reportedly manhandled by a fan and had her car attacked after last week's 4-1 home defeat by Brighton.
But Lampard did not want to use that distraction as an excuse.
"It's a difficult time. I don't have thoughts as such in that I don't want to comment on it on the back of the game, I'm more concerned about the game and that we didn't win it," he said.
"I understand the situation we are in here, I hear the noise but I have to keep working.
"The one thing I suggest, which is really important for me, is everyone involved here in every side is for Everton. We want to be successful, we are passionate about what we do.
"We need to just work in our own way to do the best and my own way is to wake up tomorrow morning and go: 'OK, let's go again'."