The 23-year-old Arsenal winger entered the Euro 2012 game with an hour played and England 2-1 down, and proceeded to score the equaliser and set up Danny Welbeck’s 78th minute winner.
Hodgson, 64, was full of praise: “Theo’s contribution was enormous.
“To come on as a sub and score such a good goal and set up a winner, he’s got to be very pleased.”
Asked if he had faith in Walcott, Hodgson added: “I believe in him. He’s a good player and has good qualities.
“I’d be lying if I said I knew the players as well as you [journalists].”
Hodgson has more than 30 years’ managerial experience but conceded that after only a month in his new job he is still finding out about his players.
“You’ve seen them play for England on so many occasions,” he told reporters.
“I’ve worked with them for one month and I’m still learning about what they’re good at and finding areas for improvement.
“I was very pleased with the performance of the two front players.”
Liverpool forward Andy Carroll started with Danny Welbeck in attack and opened the scoring in the first half before England were, according to Hodgson, “rocked on their heels” by Olof Mellberg’s left-footed strike and then subsequent header.
Hodgson brought on Walcott on the hour mark, and the Arsenal winger equalised from 20 yards with almost his first touch before setting up Welbeck for a sublime finish 12 minutes from time.
England sit second in Group D with four points knowing a point against Ukraine on Tuesday will be enough to secure a place in the last eight.
“I’m happy going into the final group game knowing a draw or win will see us through,” added the manager.
“Our goal is making certain that we continue doing what we’ve done in the four matches [Hodgson has been in charge] and not slip from that standard.”
The England coach reiterated his intention to field Wayne Rooney in the starting XI for the next game. The Manchester United striker is available after serving a two-match suspension, ruling him out of the first two fixtures of Euro 2012.
“Against Ukraine, a player like Rooney can make a major difference and I am delighted to welcome him back,” Hodgson continued.
“If I did leave him out, all hell might break loose in the dressing room.
“Rooney is a striker that sometimes drops deep like Ashley Young did in the first game [against France] and [Sweden striker] Zlatan Ibrahimovic did today. I’ll probably push Ashley to the wing when Wayne comes back.”