Hodgson, appointed on May 1 with little time to prepare for the tournament, watched on as Ashley Young's well-taken early goal proved enough to secure victory against a willing but limited Norway side.
"It was a marvellous start to my career as England manager because it's not often Norway lose at home," Hodgson told ITV after England's first win in Norway for 32 years.
"It was a great start for us. I was bit worried about the fatigue factor. People having been doing so much to impress me that I was worried that they may have left something behind on the training pitch.
"Young and [Andy] Carroll have proved they can do that job. At times we should have been more positive and got it up to them a bit sooner. That's something we've got to work on. But hopefully by the time Euro 2012 comes around we will have worked on that.
Hodgson was cautious about injury problems picked up during the match.
"I think Scott [Parker's] OK but Gareth Barry worries me a little bit more because he felt his groin so he will have to go for a scan. If it's a serious injury it's something for me to seriously to think about.
"You don't lay foundations in three days. I just think it was a very positive start to my time as manager and it keeps us going until the next game."
Manchester United's Young struck after nine minutes, displaying a silky touch to embarrass defender Brede Hangerland before finding the corner of the net with a low shot.
A low-key contest, with England missing their Chelsea contingent, fizzled out as a spectacle with Norway's best attempt an inswinging corner from Morten Gamst Pedersen that struck England goalkeeper Robert Green's near post.
Hodgson gave a debut to Arsenal teenager Alex Oxlade-Chamberlain as a second-half substitute after midfielder Gareth Barry limped off with a groin strain.
England's final warm-up match is against Belgium at Wembley next Saturday.
