The win moved the tournament hosts back to the top of Pool A, three points clear of Joe Schmidt’s Ireland.
Joseph said: “I feel very proud and a little bit relieved. The Samoan team played very well – four days after a match (against Scotland), to be able to front up, they should be very proud of that.
“We were a bit frantic in the first half and we couldn’t execute exactly what we wanted to do. But the pleasing thing is that after half-time we were back in control.
“We showed incredible belief and worked to the very end. The bench that came on in the second half had a massive impact. That’s one of the reasons we were successful.”
Japan needs to beat Scotland in their final group game in Yokohama next Sunday to guarantee qualification to the quarter-final stage.
Joseph added: “Scotland are a very, very good team, with a lot of experience and a lot of X factor. We saw how clinical they were beating Samoa last week.
“The game (qualification) was always going to come down to the final match if we did our job, and it’s building up to be a real ripper. I can’t wait, the players can’t wait.”
Samoa coach Steve Jackson was philosophical after his side’s own hopes of reaching the knockout stages were ended.
He said: “Japan were deserved winners. We had opportunities here to really put some pressure on and unfortunately we didn’t come out with the win.”
They will end their tournament against Ireland next week, and Jackson added: “We’ve got nothing to lose now, have we? Playing against Ireland – again, what an opportunity for us to beat one of the top teams in the world.
“We’ll throw everything at it. We’ll rest and recover and have a good look at this game. We’ve got a week to prepare for Ireland. We’re just going to go out there and enjoy it.”
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