In his first stint in the English top-flight, the 25-year-old managed to score just two goals in 13 league appearances for Blues before joining Fiorentina on loan in 2015.
The left-footed forward later spent two years with Roma where he notched 29 goals in 65 league outings before joining the Reds this summer for a club-record fee of £36.9million.
Salah who has been in red-hot form this campaign, increased his goal tally to 10 in 13 league games after putting Jurgen Klopp’s men ahead in their 1-1 against Chelsea on Saturday.
And Lampard who played with the forward in the London club, believes his spell in Italy played a key role in his career with Merseyside club.
"There shouldn’t be too much finger pointing [at Chelsea]," Lampard told BTSport.
"I was there with Salah, he was young.
"It was probably an early stage in his career, it didn’t work for him, he went away and did well.
“(Kevin) De Bruyne was in the same situation.
“It’s very hard - Chelsea had an abundance of talent in those positions at that time.
“So I’d rather focus on the player. Credit to them for going away, working hard and coming back.
“He’s now got more personality and a feeling of deserving to be there."
The Egyptian forward who has scored five goals in three consecutive league games, will aim to continue his brilliant form in front of goal when the Reds visit Stoke City for Wednesday's Premier League encounter.