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.
"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.
England's final warm-up match is against Belgium at Wembley next Saturday.
