The midfielder followed Maresca to Chelsea from Leicester City this summer.
"The manager was a big catalyst in wanting me to come," Dewsbury-Hall told BBC Sport.
"I knew from Leicester, a club that went down and had a lot of problems, how he managed to galvanise that, if everyone manages to buy into the system.
"I genuinely think in a short space of time we can be pushing for minimum top four - but more than that.
"He may be unknown for a lot of people, but he is top, top level. He will surprise a lot of people."
The Blues ended last season strongly but would go on to sack Mauricio Pochettino and have had their summer plans disrupted by tensions between Enzo Fernandez and Chelea's French players.
Maresca has been tasked with steadying the ship, with Dewsbury-Hall joining his former Leicester manager.
The Englishman was full of praise for Maresca, who he backs to hit new heights in London.
He also said, "You are getting lads coming up to me and asking questions. I am happy to let them know what my opinions and experiences are. They will gather their own opinions week by week.
"I remember he said to us at Leicester after six months or a year, there might be teething problems at the start but it will improve.
"Within the first week at Leicester I was convinced this was top, top level. I felt a bit stupid, I thought I knew a lot about football but he was teaching me things on a daily basis that I didn't really know before. He has an aura, he can be strict, or gentle and soft - he has both sides.
"I am getting the same feedback here with the lads. They've bought into it here from minute one which is exciting. With a system and philosophy you need everyone to buy in because, if they do, you can really achieve something."
