The Cottagers are without a win away from home all season.
“I am just disappointed we didn’t win it – our shooting wasn’t at its best,” said Hodgson.
“When Arsenal got behind us, they tested Schwarzer more than we tested (Manuel) Almunia.
“We could have made him make more saves but in general, yes, it’s a good draw for us.”
Hodgson added: “We have come here today and got a point – and that wasn’t down to a siege mentality.
“As a result, any neutrals would have seen a very entertaining game of football.”