Appearing at the Leveson Inquiry into press ethics and standards today, the Newsnight host recalled an engagement he had attended in September 2002 at Trinity Mirror's offices in Canary Wharf.
Paxman said that he vividly remembered the lunch, hosted by Trinity Mirror chairman Sir Victor Blank, as it was "so unusual" for him to be "invited into such a bestiary".
He was seated on a table with Morgan, the then editor of the Daily Mirror, along with Ulrika Jonsson, Top Shop owner Sir Philip Green, Victor Blank and the then editor of the Sunday Mirror.
According to Paxman, Morgan started "teasing" Jonsson at one stage over her relationship with former England manager Sven Goran Eriksson.
Morgan is said to have adopted a "mock Swedish accent" and claimed that he "knew what had happened in the conversations" between her and Eriksson.
"Now, I don't know whether he was repeating a conversation that he had heard or he was imagining this con. In fact, to be fair to him, I think [we] should accept both possibilities, because he probably was imagining it. It was a rather bad parody," said Paxman.
"I was quite struck by it because I'm rather wet behind the ears in many of these things. I didn't know that that sort of thing went on. Indeed, when he turned to me and said, 'Have you got a mobile phone?' I said 'yes', and he said, 'Have you got a security setting on the message bit of it?'
"I don't think it was called voicemail in those days, I didn't know what he was talking about. He then explained that the way to get access to people's messages was to go to the factory default setting and press either '0000' or '1234'. He said that if you didn't put on your own code… his words, 'You're a fool'."
Later, Paxman added: "I don't know if he was making up the conversation but it was clearly something he was familiar with and I wasn't.
"I didn't know this went on. If you were to say as a journalist you damn well should have known what was going on, I would have to accept the criticism."
Asked about the response from other guests around the table to what Morgan was saying, Paxman said: "I didn't like the atmosphere. I can't be specific, it struck me as close to bullying, teasing someone about private messages. I didn't like it."
Last December, Morgan told the Leveson Inquiry that he did not believe phone hacking ever occurred at the Daily Mirror while he was editor.
Before joining the Daily Mirror, Morgan was editor of News of the World, which was shut down in July 2011 after a string of revelations that its journalists had hacked the phones of high-profile individuals.
> Daily Mirror phone hacking possibly hidden, admits editor at Leveson