Danny Welbeck scored twice in Basel to give the Three Lions a winning start en route to France 2016.
Hodgson is delighted to have begun qualifying on a winning note, and is particularly pleased that the result came against the highest-ranked opposition in Group E.
"I think it will give them a lot of confidence," he told Sky Sports News. "I think this was an important one to play well in because some of the games we have coming up, especially at Wembley against lesser opposition, if players had played well in those games, there would be a tendency to say, 'Wait until a big team comes along'.
"But here, I think Switzerland haven't lost a qualifying match here since England beat them four years ago, so this was always going to be a tough ask. I thought the players stood up to it very, very well. We really got our rewards tonight.
"I thought even in the first half that we should be leading the game, we had a couple of very good chances early in the second half that we missed, but fortunately we took the one that really put is in the ascendancy and were able to aggravate the score at the end."
Hodgson added that he felt England can still improve ahead of October's qualifier against San Marino.