Australia made relatively solid totals of 207 and 201 and skittled out Sri Lanka for 97 and 162 to win by 149 runs.
"We probably just were able to bat just a little bit better than they did," Gilchrist told a news conference.
"Both teams bowled in the right areas, but there were a couple of periods where we were able to build a partnership in both innings.
"(Darren) Lehmann with a 50 in each innings (57 and 51), it was probably like a hundred in each innings in any other Test match. We were able to apply ourselves a little bit better when it was up for grabs."
Gilchrist, who stood in as captain for Ricky Ponting who missed the match after a family death, top-scored in the match with 80 in Australia's second innings.
Sri Lanka captain Marvan Atapattu, who opened and made only four and 10, said: "It was difficult to handle as a batsman. On a wicket like that, nobody was really in (looking at ease)."
However Atapattu added: "Taking 20 wickets for just over 400 runs playing against Australia is a very positive thing."
Right-arm seamer Michael Kasprowicz took seven for 39 in Sri Lanka's second innings, his second-best career figures.
Injuries to Brett Lee and Glenn McGrath gave the Queenslander the chance to return to Test cricket in March this year in Sri Lanka after three years on the fringes.
The 32-year-old Kasprowicz responded with 12 wickets, the best haul by an Australia fast bowler in the three-match series.
"For me having played before for Australia and tasted it, I was obviously pretty keen to get back," said Kasprowicz, who has taken 66 wickets in 21 Tests.
"I have no doubt I am a far better player than I was last time I played for Australia. As you get older, you learn what you can do and what you can't do."
