The Poland Under-21 international was Pellegrino's first signing after replacing Claude Puel as boss in June.
"He's a very good coach and person, and so far he has already helped us so much," Bednarek, 21, told BBC Radio Solent.
"I think he has a different view on football - I think we can achieve a lot with him."
Saints endured a mixed pre-season under the Argentinian, but beat Sevilla 2-0 at home in their last fixture, having lost 4-0 at home to German side FC Augsburg.
In addition to Bednarek's arrival from Polish side Lech Poznan for £5.7m, Saints have signed midfielder Mario Lemina in a club record £18.1m deal from Italian champions Juventus, with both in line to make their debuts in Saturday's Premier League opener against Swansea City.
"Swansea are a good team, but it's most important to focus on our team, to prepare the best we can," said Bednarek.
"We have to analyse their game, which is normal, but most important is how we'll play. If we play well I'm confident we'll win."
Southampton defender Jan Bednarek believes the club can enjoy success under new manager Mauricio Pellegrino.