The 31-year old striker came onto the Wembley pitch in the second half for his first international only to score two minutes later to give England an eventual 3-2 friendly victory over Scotland.
Hodgson was delighted for the Southampton star who was taking part in just his first Three Lions squad.
"He's been so enthusiastic. He's been like a young boy with a new toy ever since he joined us," Hodgson told ITV.
"We believe in him and, funnily enough, when he came on the first thing [England coach] Gary Neville said to me was 'he's going to get us a goal'. He almost got us three - he certainly got us a very good one and was very close to two others.
"I'm delighted for him. He's a man who's worked very, very hard for this chance and done it the hard way, and now he's crowned his debut with a goal.
"He's technically a very good player and has great composure in front of goal, as we saw today."