Substitute Andros Townsend rescued a draw for England in Turin, coming off the bench to equalise with 11 minutes remaining.
Townsend's spectacular strike capped an improved second half for the visitors, who trailed Italy following Graziano Pelle's 29th-minute header.
While Hodgson was disappointed with England's first-half performance, he saluted their response after the break, singling out substitutes Ross Barkley and Townsend for praise.
"I am satisfied with the result, as it is never easy to win in Italy," he said.
"But most of all I am satisfied we were able to pick ourselves up after that performance in the first half that fell way below what we are looking for.
"I thought the second half was good but the first half was nothing like what we want to see from our team. The game was dead to be perfectly honest, I thought it was a very dull affair.
"We set high standards these days and we got nowhere near to matching them in the first half in terms of the way we want to play, the tempo and intensity of our play, all of those things that have served us in good stead recently.
"But I am fortunate that we put it right at half-time, we had a terrific injection from two young players in [Ross] Barkley and [Andros] Townsend, which was very useful performances from those two for us, and I thought in the second half we actually played quite well."
Hodgson also paid tribute to young striker Harry Kane, who completed his first 90 minutes for England in his second appearance after scoring on debut against Lithuania last week.
"I thought Harry Kane did very well," the 67-year-old added.
"It wasn't an easy game, playing against three very experienced, tough defenders. He got helped a bit more when Wayne [Rooney] went up front, but I'm more than satisfied personally with his performance.
"It's been a good 10 days for him. He's scored on debut and played 90 minutes of a tough game. He'll gain a lot of benefit from that."
Thank you for reading 5 articles this month* Join now for unlimited access
Enjoy your first month for just £1 / $1 / €1
*Read 5 free articles per month without a subscription
Join now for unlimited access
Try first month for just £1 / $1 / €1