The tourists eased to an eight-wicket win in the second and final Test at the P. Sara Oval in Colombo on Saturday to make amends for the 75-run loss in the first Test in Galle, which was their fourth straight Test defeat this year.
England's losses, including an embarrassing 3-0 whitewash at the hands of Pakistan in the United Arab Emirates, had left them teetering on the brink of losing their top ranking.
The one blemish in the hard-fought series against Sri Lanka was Strauss's own batting form. He made just 114 runs in four innings at an average of 28.50.
The left-hander appeared to have found his rhythm when he hit 61 in the first innings of the second Test, but he fell for a duck in the first over of the second innings as England chased a modest target of 94.
Strauss has not added to his 19 Test centuries in 25 innings and has just one three-figure knock in his past 50 innings, raising questions about his future in the side.
But the skipper said he had never doubted himself or his leadership role.
"I never had any doubts about whether this was the time for me to go," the 35-year-old veteran of 94 Tests said, adding he was focused on his side performing well.
"I am very determined and committed to seeing us improve as a side. It's been an interesting week or two, but we as a side should not get carried away with whatever the issue of the day is.
"We have done that very well over the last couple of years, and obviously I needed to do it in this Test. We needed to do it as a team and I thought we did it well."
Strauss admitted England had been under pressure after their four consecutive defeats but was delighted the hard work had eventually paid off.
"We had to make sure we learnt the lessons from our defeats over the last four Test matches," he said.
"I saw a steely determination on everyone's part to make sure we finished the winter on a high and it was fantastic to be able to do that."
Off-spinner Graeme Swann's match haul of 10 wickets left England chasing just 94 to win, which they achieved easily despite slipping to 31-2 after the dismissals of Strauss and Jonathan Trott.
Alastair Cook remained unbeaten on 49 and Kevin Pietersen, who hit a century in the first innings, smashed 42 not out off just 28 balls, bringing up the win with a six off Tillakaratne Dilshan.
"They are horrible chases because everyone expects you to win," said Strauss. "It's almost like trying to sink a three-foot putt. You know it should go in but it doesn't always."
The number one ranking will remain on the line as England return to the comfort of home conditions for Tests against the West Indies and number-two ranked South Africa.