The new Three Lions captain scored the winning goal from the penalty spot in his country's first outing since the World Cup but struggled to involve himself in open play.
Rooney scored from the spot after Raheem Sterling had been brought down in the box but was otherwise largely anonymous at Wembley, with the Liverpool winger taking most of the plaudits for a far brighter display.
A visibly irritated Hodgson argued that Rooney's compatibility with Daniel Sturridge could not be judged on the evidence of one friendly match against a Norwegian side who he felt had set up to frustrate his team.
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"The fact is that it was a big night for Wayne and a lot of responsibility," the manager told reporters. "He's got to step up and make sure he scores the penalty to give us the victory we really want.
"It's early days [for his partnership with Sturridge]. If every time we play a game I've got to praise a player to the skies or criticise him and say it's not going to work, I think that's a little bit harsh.
"He can play better than that, of course he can, but we know what he's got to give."
Hodgson praised Danny Welbeck after the new Arsenal signing made a positive impact as a late substitute but pointed out that, by that point, Norway was forced to push forward in search of an equaliser.
"When Danny came on with James Milner and Fabian Delph, we were leading 1-0," he observed. "In the first half we were playing against team not making too many attempts to attack us and defending well, making terrific blocks. It's not always right to compare performances in the first 25 minutes of a game with the last 25 minutes.
"But I am very happy with Danny Welbeck and, when Sterling moved into the center, he showed his full range of dribbling ability. It's nice to know we won't just be restricted to one way of playing."
The former Fulham boss believes that England will be forced to do more defending in its opening Euro 2016 qualifier against Switzerland on Monday - and even conceded that it may bear more of a resemblance to Norway in this fixture - but hopes to exploit the space that opens up as a result on the counterattack.
"We aren't [currently scoring lots of goals] but we're playing against teams that aren't coming out at us an awful lot," he added. "We'll score goals - Rooney's got goals, Sturridge has got goals, Sterling's got goals.
"If anything we might be more like Norway on Monday because we're pushed back and can't attack and dominate the game as we did for large periods today. I don't know - maybe not - but I don't think the mindset of the Swiss team at home in Basel will be the same as the the Norwegian team today."
Much was made in the buildup to the game of the crowd of little more than 40,000 fans at Wembley and, while Hodgson took time to praise the supporters that did attend, he conceded that the caliber of teams in England's qualification group may not encourage larger audiences in the future.
"I think you'll find that we'll find it hard to bring [attendances] back to a very high level because the opponents we're playing aren't going to excite the public," he explained. "They're not the type of teams that attract full houses.
"If the team can work as hard as they've done tonight and show the appetite and exciting moves that were on the field for all to see, the crowds aren’t foolish. They know what they're seeing.
"I'd like to think they'll be back to see more of Sterling, Sturridge, [Jack] Wilshere and all the others. I believe these players have got the potential to lead us forward.
"I've been watching football for a long time and nothing that you say is going to change my mind on what I see."