England have taken "big strides forward over the last eight months", said captain Alastair Cook after his side eased to a 241-run victory in South Africa on Wednesday.
The visitors claimed six wickets for just 38 runs on day five to win the first Test in Durban.
England regained the Ashes this summer but lost to Pakistan last month, winning six of their 14 Tests in 2015.
"Potentially this team can do some really good things," Cook said.
"There's so much talent in this side but it will take relentless hard work."
Cook said the tourists will have to guard against a South Africa backlash in the next match, starting on Saturday in Cape Town, where England have not won since 1957.
"It can turn very quickly. They have world-class players so we can't get too carried away," he said.
"But it would be nice to get our noses ahead again and to continue to put pressure on South Africa."
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Cook on Compton
Nick Compton's grandfather Denis played in that 1957 victory by 312 runs, and Cook was full of praise for the current England number three's patient 85 from 236 balls in Durban. He had been out of the Test team since May 2013.
"The way Nick played really set up the first innings," Cook said. "He was a rock for us in that first innings. From that moment on, the guys bowled particularly well to take 20 wickets and we scored enough runs in the second innings."
Anderson optimism for Cape Town
James Anderson, England's leading Test wicket-taker, missed the Durban Test with a calf injury, but was seen bowling at the ground before the final day began.
Asked about the swing bowler's chances of being fit for Cape Town, Cook said: "He has had a tough week, bowling a lot and doing rehab. Hopefully he'll be fit.
"He is hopeful of playing and it's looking good but we'll know in the next 48 hours.
"We know what a strong side South Africa are in home conditions - but we're really prepared for this tour."
Meanwhile, England wicketkeeper-batsman Jonny Bairstow was delighted to claim the team's first stumping for 38 Test matches when he dismissed Temba Bavuma, having spilled a chance to stump AB de Villiers the previous day.
"It doesn't necessarily make up for it because I was desperately disappointed to miss it. You work so hard on your game that when the opportunity arises you like to take it," he told BBC Test Match Special.
"To get another one and get into the game was really pleasing and something I can take forward."
Asked about South Africa's batting frailties, he said: "They are not the number one side in the world for nothing and have proven over a long period how good they are.
"We've got to be mentally and physically prepared for what is going to be a very tough battle in the New Year Test match."