Jonny May scored two tries and Mike Brown also crossed as England ended a five-match losing streak by securing a 28-9 victory at Twickenham on Saturday.
Questions had been raised over head coach Lancaster's future following four defeats to New Zealand and then another loss against South Africa last weekend.
Lancaster made five changes to his side following that defeat to the Springboks, the most notable being George Ford making his first start and the fly-half responded with an encouraging performance.
Australia will be England's final opponents this month when they visit Twickenham next weekend and Lancaster is happy to put talk of his side's losing run behind them ahead of that game, but is aware there is work to be done.
He told Sky Sports: "It does feel good yes, it had been long time. I'm delighted with the win, but there still areas we could improve on and I think we recognise that.
"I thought Samoa were very good in terms of physicality, intensity and aggression.
"When you look back there were one or two opportunities at the end that we didn't take.
"I'm delighted with George Ford and Anthony Watson, two young lads who've done well."
Ford scored 13 points with the boot and his intelligent kick for Watson resulted in Brown powering over in the first half.
Lancaster is predicting big things from the 21-year-old after his impressive showing.
He added: "It was a great first start, he's a young player and we need to look after him because he's going to be a very big player for England."
The head coach revealed that Courtney Lawes' fitness will be assessed after he suffered a knee problem.