David Ngog struck twice as Hodgson began his reign with a comfortable win in the first leg of a third round qualifier in Skopje.
The ease of victory fully justified Hodgson's decision to leave behind the likes of Steven Gerrard and Joe Cole.
"I am very satisfied," Hodgson said.
"It was a game that could have been very difficult for us.
"It was a big crowd and some of our players that played are not used to big crowds.
"I was really pleased with the way everyone went about their business and we can go back to Anfield with a margin of victory which will enable us to feel a little more comfortable."
Hodgson, who was appointed a month ago, was pleased to have made a winning start in his new job but did not feel as if a great weight had particularly been lifted.
He said: "I feel like I've been up and running for the last four weeks.
"I have had a very hectic and busy month - it has been a month where my feet have not touched the ground.
"I fear having taken on this job there will be a weight of expectation on my shoulders every time I step into Melwood for a training session, every time I go to a game with the team.
"I came to the job knowing that was the situation and the important thing is to put a team capable of meeting that expectation."
Liverpool were without 10 World Cup players for the tie as they have either only recently returned for pre-season or are still on holiday.
That left just a handful of senior stars in Lucas, Martin Skrtel, Daniel Agger, Alberto Aquilani and double goalscorer Ngog. That allowed youngsters David Amoo, Jay Spearing and Martin Kelly a chance to impress.
Hodgson said: "Every time a team plays in an official match you learn a lot about people.
"And there were a lot of players out there I need to learn about as some of them I have hardly worked with.
"It was a very good exercise for me in that respect and I am delighted for so many players who were under pressure before the game that it has been a positive outcome.
"They can go back to Liverpool tomorrow feeling positive."
Rabotnicki coach Zoran Stratev felt his players had given their all but were perhaps intimidated by the reputation of Liverpool.
He said: "Our players gave their maximum.
"They were very good at times, especially in the first 15 minutes, but I think they were scared by the name of Liverpool.
"But I don't have any complaint about our players.
"They played as well as they could but we know Liverpool are a better team than us.
"Now we have the return match next week and we know our chances will be minimal.
"Liverpool came with their second team but they are all still good players."