Victory over Southampton was West Ham's fourth on the bounce.
Allardyce said: "The worst week was when we lost to Forest [5-0] and then [6-0 to] Manchester City. But that was in the cups, so it proves my point again, doesn't it? That's why I'm good at what I do, isn't it?
"The cup is not the material thing, the Premier League is - for everybody apart from the top four. They need to win the Premier League and get into the Champions League, everybody else needs to stay in the Premier League first and go for other things after that.
"I don't need to feel vindicated, I'm just doing my job properly."
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