The result comes on the back of England's early World Cup exit and disappointing friendly display against Norway, and Hodgson is glad that his side were able to produce a winning performance against arguably their toughest Group E opponent.
He told Sky Sports News: "I think every win is important and every game as England manager is unbelievably important.
"I think it is a very honoured and privileged position and every time I lead an England team out or an England player puts a shirt on, it doesn't matter if you're playing Switzerland away or San Marino at home, it's a big occasion.
"I agree that this one had a special importance because we needed to play well and get a result against a team, strangely enough, ranked higher than us at the moment."
England face San Marino in their next qualifier in October.