The 34-year-old trailed 1-0 and 2-1 and despite going in level at 2-2 at the mid-session interval after two 50-plus breaks, he was not happy.
"There was lot riding on it and it took me a little longer than I anticipated to settle down.
"Even though I made a good break to go 1-1, I just never felt I had completely settled," said the world number 24.
The Londoner produced a magnificent 131 in the fifth frame and added two more to make it four in a row and leave him needing just one for victory at the York Barbican.
Northern Ireland's Swail, the world number 58, pulled one back, but Gould's fourth half-century of the match secured a quarter-final meeting with David Grace.
Gould, who had never previously been beyond the second round of the UK Championship, added: "I was pleased to come out at 2-2 after the interval. And I said to myself it was the time to step up.
"The 131 was the first frame after the interval and that gave me the impetus to carry on.
"I got in to a rhythm and a stride and when I get I am quite hard to stop. It was important for me to stamp my authority on the match."
Leeds potter Grace, who is ranked 81 in the world, beat former world champion Peter Ebdon in the fourth round.

The president scrapped sanctions implemented 11 years ago against former President Charles Taylor.
Taylor is now in a  maximum-security prison for a series of war crimes.
President Obama said that Taylor's imprisonment meant that sanctions were no longer necessary.
He said that he and his allies now had a "diminished ability" to "undermine Liberia's progress".
National Security Council spokesman Ned Price said that the US wanted to congratulate the people of Liberia "for their determination, ingenuity and commitment to peace and democracy" that has made the lifting of sanctions possible.
Taylor and his inner circle fuelled a brutal 1991-2002 civil war in Liberia that killed tens of thousands of people.
He was arrested in 2006 and charged by a UN-backed court with 11 counts of war crimes and crimes against humanity for acts committed by rebels in Sierra Leone who he aided and abetted.
The Special Court for Sierra Leone trial was held at The Hague in case it sparked renewed unrest in West Africa.
Taylor was sentenced to 50 years in jail for what judges described as "some of the most heinous crimes in human history".
The former Liberian leader is now being held in a maximum-security British prison.
Liberia has been led by Nobel Prize winner Ellen Johnson Sirleaf since 2006. She has worked closely with the West in tackling Ebola.
Martin Gould said he felt the pressure in the early stages of his 6-3 last-16 UK Championship win over Joe Swail.
[NEXT_CONCEPT]
The US has lifted economic sanctions against Liberia as President Barack Obama praised the country's commitment to democracy since the end of the 2003 civil war, the White House has said.