Winstone, 55, an East Ender and life-long Hammers fan, was impressed with Andy Carroll's swashbuckling debut last week and believes Big Sam should get the credit for his snatch of the day.
He told the Daily Star Sunday: "Sam has done well. He has brought steel and heart to the dressing room.
"We are going to need that if we are to do well in the Premier League. We look all right. There are one or two teams in the league who don't look all right and that's great for us.
"Survival in the Premier League is obviously what we want.
"I was very worried at the end of the last one. We were very lucky to come up in the Play-Off Final. Blackpool were the better side but thank God they couldn't finish!
"We did it. We had some dodgy moments and some draws at home we could have done without. But the thing I loved about the side was that they had heart.
"I think that had been missing for a few years. I am not talking about players like Mark Noble - who would die for the club - but some others."