The Blues appointed Lampard as their new boss last week after the 41-year-old signed a three-year deal with the west London club to replace Maurizio Sarri.
Sarri led Chelsea FC to a third-placed finish in the Premier League and Europa League glory last term before opting to leave Stamford Bridge to take over at Juventus.
Lampard has now been tasked with steering Chelsea FC into the top four next season as they look to try and challenge for trophies in his first campaign in charge.
Arsenal will also be looking to finish in the top four next season after they ended up fifth and without a trophy last term.
And Cascarino feels that the Blues are better placed to finish above the Gunners because they have a better squad at their disposal.
Speaking in an interview quoted by the Daily Express, Cascarino said: “He [Lampard] has got a better squad than Arsenal so he’s going to have to be expected to finish in front of Arsenal.
“You could argue the top four, where people are looking and going ‘oh well, maybe they won’t get in it, they may have to sacrifice this season, I don’t believe Chelsea Football Club will do that.
“If you go through their team and you go from the goalkeeper, Kepa, decent keeper.
“Then you go right-back, [Cesar] Azpilicueta, good defender, [Antonio] Rudiger, good defender.
David Luiz has his moments but is still a very fine, experienced defender.
“Then go through their team and we look at [N’Golo] Kante in midfield, you can’t get a better holding midfielder than him and it just goes on and on and on with Chelsea.
“So to make too many excuses before you get to the end of the season and say ‘well this was always going to be a transitional year’…
“Yes, we all understand that Liverpool and Man City are quite clearly a long way in front of the rest.”
Arsenal lost 4-1 to Chelsea FC in the Europa League final last term as they missed out on a trophy and Champions League qualification.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news