Marsch last week suggested Lampard did not rate United States international Pulisic when he first arrived at Stamford Bridge due to his nationality.
Speaking to Extratime Radio, the American said: "I could see right away that Lampard's idea of Pulisic was shaped a lot by the fact that he was from America.
"When I spoke to him in pre-season a year ago, I was talking to him about having Pulisic and he was kind of like, 'Yes, he's got a lot to learn so we'll see how he does'."
CHRISTIAN. PULISIC. 💥 pic.twitter.com/nNkgqGr3BP— Champions League on CBS Sports (@UCLonCBSSports) October 28, 2020
Pulisic has made a big impact during Lampard's 15 months in charge, playing a direct part in 13 Premier League goals since the start of 2018-19.
Only Tammy Abraham (19) has managed more among Chelsea players still at the club, while his 2.75 dribbles completed per game is bettered only by Mateo Kovacic (3.19).
And after getting off the mark with his first goal of the campaign in Wednesday's 4-0 win over Krasnodar, Lampard reiterated he has never questioned the winger's ability.
"I did read those comments. I was surprised that Jesse read my mind as well as he did!" Lampard said ahead of Saturday's Premier League trip to Burnley.
"It was a game against Salzburg when Christian scored twice in pre-season. I said it was exciting to see how he'd develop with us but Jesse put it across a little differently.
"Maybe Jesse knows the feeling of American managers coming into Europe. I played in America for 18 months and will never underestimate the desire those players have.
"Christian has that and incredible talent so it was never in doubt for me. I understand the rigors of it. It's the toughest league in the world to play.
"What Christian did was find his feet quickly and had a great breakthrough season. His performance was massively impressive.
"He'll get better and better because he is a young player. I never doubted him. It's important for me to put that straight."
On the back of successive goalless draws, Chelsea found the perfect balance between attack and defence in their Champions League Group E win over Russian side Krasnodar.
Hakim Ziyech marked his full debut with a goal while fellow attackers Callum Hudson-Odoi, Pulisic and Timo Werner were also on target, the latter netting from the penalty spot.
Lampard has once again talked up the importance of making full use of his large squad with three more games to play over the next 10 days.
"Hakim was very good last night, so that was a big plus," he said. "The other teams, particularly those in Europe, are also finding the schedule heavy. We need options.
"We're also searching for relationships as newer players are learning about each other and how we play. There will be rotation at times. We need everybody."
Thiago Silva did not make the trip to Russia but Lampard will bring the experienced defender back into his squad for the meeting with Burnley.
"He is fit. Taking him out of the squad for Krasnodar was a maintenance issue," he said. "It made sense to leave him out.
"As a player towards the end of my career – and I'm not saying that's the case with him – it's about making sure we get the best out of him towards the end of the season.
"I spoke with him and he could have played if he had to but I had to put it in context of what is ahead of us."
Chelsea have won five of their six Premier League away games against Burnley, scoring at least twice in each victory.