Pulisic officially signed for Chelsea from Borussia Dortmund in January 2019 when Maurizio Sarri was at the helm of the West Londoners, but stayed at the Signal Iduna for the remainder of the 2018/2019 season.
The USA international joined Chelsea ahead of the 2019/2020 season when Lampard was newly appointed as the Blues head coach.
Pulisic scored twice against Salzburg in a 2019-20 pre-season game but eventually had a slow start to life in England.
The 22-year-old has since established himself as one of the most important players in Chelsea.
“I did read the comments and I was surprised that Jesse had managed to read my mind as well as he thought he did," Lampard told reporters ahead of a trip to Burnley this weekend.
"He’s recounted the conversation wrong, I have to put it correctly because it was the game against Salzburg and Christian scored two goals in pre-season. Fair enough, Jesse came up to me and said what a talented player Christian was which I knew and I agreed with.
"I spoke about the fact it was so exciting to see how he could develop for us with the talent he has. That was the conversation. Jesse managed to put it across slightly differently.
"Maybe Jesse knows the feeling of American managers and coaches that travel into Europe, but one thing I did have was I played in America for 18 months and I would never underestimate the desire that American soccer players – football players – have to learn, to improve, take on information and understand the technical side of the game.
"So when you have that, which Christian had, and you have incredible talent, it was never in doubt for me. My only thing is I coach in the Premier League and have played here for nearly 20 years so I understand the rigours of it.
"That brings me on to Christian’s development last year. It is clearly the toughest league in the world to come and play at a young age from a different league. It is not just Christian who will have felt that in the early stages.
"Some of the greatest players in Premier League history, whether they came from America or Europe or anywhere in the world, have felt that.
“What Christian did was find his feet very quickly and have a great first season in the Premier League where he produced goals and assists.
"I thought his performance last season was massively impressive.
“He will get better and better because he is a young player but I never doubted him in the first place, and that’s not me jumping on Jesse because there’s probably a bigger issue there with American players.
"I don’t want to comment on that – he can field that one himself – but as a manager I never doubted Christian and it is important for me to put that straight actually, more for Christian than anything."
