Jarosik, who played alongside Lampard in the 2005/06 season, feels his old team-mate needs to strengthen his squad even further when the transfer window reopens.
“Going from Derby to Chelsea is a different pressure," he told Goal.
“Chelsea is a phenomenon now and one of the biggest clubs in the world so this job won't be easy.
“From the start he was in a difficult situation without being able to bring in players. They have gone with a young team.
“If they want to compete for the title, I think they need some players with more experience because the Premier League is very difficult.
“They have become inconsistent which is something that comes with youth and the quality of the league.
“A lot of guys have come [back] from smaller clubs on loan to Chelsea.
“I think Chelsea will scout well ahead of the transfer window having not signed anyone yet.
“I think they need more than one player in Hakim Ziyech because they need a bench that can help them compete for a title too. They need to be stronger to win the biggest games."