The Hammers boss and his team were booed by fans at Upton Park, despite securing a 2-1 victory over 10-men Hull City on March 26.
"West Ham fans are used to watching good football I guess, but I don't think we have got the players for tippy tappy football," Winstone told talkSPORT. "We have been relegated playing that sort of football before.
"Sam has come in to do a job. He has made us tougher. We are in mid-table and, I tell you what, at the beginning of the season I would have taken that."
Winstone is currently promoting his new film Noah.