Wales trailed 10-6 at half-time but remain on course for a potential last-eight clash with Ireland thanks to a second-half try from Shane Williams sparked by the invention of James Hook's replacement Leigh Halfpenny.
"It was a tough match and I thought we showed some great character," Gatland said after the 17-10 win.
"We were under pressure at half-time but the boys dug deep and showed some real character after last week's disappointment (the narrow loss to South Africa).
"We've worked really hard the last few months and you've got to show people how much it means to us to get out of this and get a W (win) on the board.
"I thought in the last 15-20 minutes Samoa's conditioning probably told and they looked to tire a bit and weren't quite as effective in the second part of the second half as they were in the first.
"I thought we defended exceptionally well for most of the game."
Wales certainly needed to, with Samoa stopped inches short of the Welsh line on numerous occasions.
Captain Sam Warburton dedicated the win to the families of the four miners killed in the flooded Gleision Colliery near Pontardawe.
"We said if we lose the chances are we're probably going home so there was a lot of pressure on the boys and I would like to dedicate the win today to the families of the miners back home," he said. "Our thoughts are with them."
As for the game itself, Warburton added: "Both sides didn't disappoint, we knew it was going to be an immensely tough battle. Samoa are very physical and it was a tough game for us.
"We wanted to keep the ball in play as much as we could and back our fitness levels towards the end of the match.
"Leigh came on and added some great momentum to the side and Shane finished it off as we've seen him do a million times before. If our backs get a sniff they're pretty handy."
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