There was a febrile atmosphere within Goodison Park after Everton conceded three goals in seven second-half minutes to slump to a dispiriting defeat which has left them 18th in the Premier League.
Although the focus shifts to the FA Cup ahead of Friday's third-round tie away to Manchester United, the pressure is firmly on Lampard as the Toffees face the prospect of another relegation scrap.
Lampard said the nature of conversations he had with the club's hierarchy on Wednesday would remain private, but added that he did not need to ask about his own position despite the perhaps itchy finger of club owner Farhad Moshiri, who has sacked five managers in almost seven years.
"I will never and would never seek reassurances," Lampard said. "It's part of my job to focus on the job in hand, day to day, game to game. I don't need reassurances. I come to work to try to improve a bit every day - myself, the team, the squad and everything.
"I'm not hunting around for any reassurances."
Lampard added that the club's league position was not his immediate concern, saying he was focused on a longer-term process.
"If we win the next league games, we'll be out of the bottom three probably," he said. "It's part of the process. I'm very aware of what I came in to do in this job. I want to be a success at this club.
"Any challenges that come along, then I'll take them on and actually enjoy them.
"I enjoy working for this club, it's a real honour for me. That's why I say 'I don't need reassurances'. I'm a big man working for a great club and I'll keep doing it."
Everton's problems stretch back much further than the 11 months Lampard has been in charge and many fans have directed their anger at the club's board for what they perceive as years of mismanagement.
Lampard took over last January after the ill-fated appointment of Rafael Benitez, inheriting a club that was 16th in the table at the time. Despite what the league table might say, he insisted he has brought about improvement in the time since.
"I wasn't expecting huge change," he said. "Every improvement would be step by step and then maybe one day you go, 'Oh, here it is, here's what it looks like'. But in my opinion, yes (there's been improvement)."
Everton will now look to the January transfer window to help them take the next step. Lampard would not be drawn on links with Aston Villa's Danny Ings, but an attacking player is a priority.
"Both options are on the table in terms of loan or buying players," he said. "I'm never going sit and talk about finances because I can't give you the detail.
"We want to improve the squad in January but my job is first and foremost to work with the players we've got and try to get a result against Manchester United and Southampton.
"If we can improve and help the squad, great. It's not an easy window, everyone knows that but certainly we'll try to improve the squad because it feels like we need that for sure."
Nathan Patterson faces six weeks out after suffering medial ligament damage on Tuesday.
"It's a blow, a freak one in terms of how he did the injury," Lampard said. "It's a big blow. He's a young full-back. He's come in, broken through and done well for us.
"It's time for others to step up to that mantle. Six weeks sounds a long time but he'll be back."
Anthony Gordon remains a doubt through illness but Yerry Mina has recovered, while Dominic Calvert-Lewin must also be assessed after suffering with fatigue.