Replacement hooker Pita Godinet scored two tries in seven minutes to put Samoa within touching distance of a shock triumph.
But Sam and Joel Tomkins made the most of spiralling kicks from scrum-half Matty Smith and a touch of good fortune to touch down before England then repelled a furious final assault from the Pacific Islanders.
"It was a tremendous game if you're a neutral watching that," McNamara told a post-match media conference.
"We're certainly relieved to get the win. I knew that sort of game was coming. We're a brand new team practically.
"We've travelled from one side of the world to the other. We've had nine days to get ready.
"[It was] pretty extreme conditions for an Englishman out there and tremendously tough against a Samoan team that I thought were really, really good.
"We had to dig ourselves out of some dark places at times to come up with the win.
"We've been in these situations before, where we've been on the wrong end of the result.
"We've got the win, we've got so much improvement left in us, hopefully, and we know we'll need to do that for next week."
Tries from Michael Shenton, Kallum Watkins and Liam Farrell meant England held a 20-10 lead in the second-half before the Samoans set in motion a thrilling finale.
England unquestionably need to smooth out elements of their performance ahead of next weekend's clash with Australia but acting captain James Graham preferred to focus on the positives of a battling display.
He said: "We had to hang in there at times and come up with some big plays. Sam Tomkins' try off the bomb when Shenty [Shenton] knocked it back, that was a huge play for us and credit to the boys for coming up with them.
"It would have been awful to lose, you never want to come away from any game losing but we're just taking it one week at a time. We've got this first week out of the way.
"We'll go back, review it and start to look towards Australia. There's no point looking too far ahead.
"For 80 minutes we weren't perfect but we showed a lot of good signs there. This isn't an excuse, but we've been together a week less than other teams with the Super League Grand Final going a week later."
"We came together as a group, we set some targets and we wanted to get this win. So we've got to be happy with that."