Johnson completed a £47.5million transfer to Spurs in the final minutes of deadline day and has not yet played for his new club.
But Williams said the 22-year-old forward celebrated the move by taking several of his Wales team-mates out to dinner in London and picking up the tab.
Johnson is, perhaps unfairly, considered the direct replacement for record Spurs goalscorer Harry Kane and the man to fill the boots of retired Wales great Gareth Bale at international level.
“A lot fans will say that, but at the same time Brennan is not Gareth Bale or Harry Kane,” Forest full-back Williams said ahead of Wales’ vital Euro 2024 qualifier in Latvia on Monday.
“He’s his own player and he has got his own style. He wouldn’t want to be compared to them or be seen as their replacements to step in.
“He has got the potential to reach the highest of levels. But at the same time he’s only 22 and still very young.
“He has proven it in the Premier League and now he has to prove it at what you’d say is a top-six team and do it in the Premier League again.
We can't wait to see you out there, Brennan pic.twitter.com/ubb3LPso4R
— Tottenham Hotspur (@SpursOfficial) September 4, 2023
“He’s got a move for big money and you can see that his confidence has taken him to the next level.
“Hopefully he can take that with him into this Wales camp and win us some games.”
Johnson met up with some of his Wales colleagues in London after joining Tottenham before arriving for international duty.
“We celebrated with a little drink and some nice food,” said 22-year-old Williams.
“It was a little meet up and a chance to say congratulations to Brennan on his move. To be fair, he got the bill as well.
“Everyone was buzzing for him. It was last minute but we are all very pleased for him.
“I’m just not looking forward to seeing him come back to the City Ground!”
Johnson and Williams both started on Thursday as Wales drew 0-0 with South Korea in a Cardiff friendly.
But the Latvia game represents the important part of the September double-header as Wales attempt to revive their Euro 2024 qualification bid.
Defeats to Armenia and Turkey in June have left Wales playing catch-up in Group D and there is no margin for error in Riga.
Williams said: “When we look back on it, the goals we conceded, we know we can do so much better than that.
“As a team, that just wasn’t us. You can pinpoint so many things.
“The gaps were too big from the strikers to the defenders, it just wasn’t a good performance all-round.
“We’ve got top teams in our group and knew it wasn’t going to be easy from the start.
“But we’ve got plenty of games to put that right and get as many points as possible to qualify.”