Potter said he had been targeted by an anonymous account following the team's recent poor form, which continued with a 1-0 home defeat by Southampton last Saturday.
Afterwards some supporters behind the dugout at Stamford Bridge called for the manager to leave, with the atmosphere turning increasingly hostile as the game wore on.
Personal attacks on social media have also increased following the loss to the Saints, but those have now escalated to threats being sent to him directly.
Potter, who has said previously he believes he has the hardest job in football, was nevertheless visibly upbeat ahead of his team's trip to Tottenham on Sunday, joking he was late as he had been at a "crisis meeting" with the club's owners.
He spoke of the toll the recent months have taken on him personally, and bullishly rejected accusations a calm demeanour in the face of adversity means he does not care about the club.
"If you go to work and somebody's swearing abuse at you, it's not going to be pleasant," said Potter. "You can answer it two ways. I could say I don't care, but you know I'm lying. Everyone cares what people think, because we're hardwired to be socially connected.
"I want to succeed here. There's nonsense (being said) that I don't care. Where does that come from? Where's your evidence on that? Ask my family. People have a perception I don't care - what's that based on? How do you know?
"You could ask my family how life has been for me and for them. It's been not pleasant at all. I understand supporters go home and they're annoyed because the team aren't winning. But I assure you, my life for the last three or four months has been fairly average.
"I've had some not particularly nice emails come through, that want me to die and want my kids to die. That's obviously not pleasant to receive. If you've been asked for four months if you're under pressure, because (the media) need to sell stuff - what do you expect, in the end?
"You know there's a problem when the email address it's been sent from is 'Potter bastard at Gmail dot com'."
While Potter acknowledged only wins will turn the tide of opinion, he was determined not to buckle under the weight of abuse.
"Life is tough for lots of people," he said. "No one really wants to care about Premier League managers. Sometimes life isn't fair. It's not like I'm complaining about it. You ask me is it hard, I say yes it is hard.
"You suffer. You get upset. When you're in private, you show real emotion with your family.
"There's a point to be considered, but the world is tough. We're going through an energy crisis, a cost of living crisis. People are striking every other week. No one wants to hear about the poor old Premier League manager.
"My job is to act how I think I should act in the best way for Chelsea, act with integrity that is right for me. I don't want to be anybody else. I don't want to be fake. I'll be me, and I'll do my best. If my best isn't good enough, I accept that."
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