Campbell, who underwent surgery on his foot just seven weeks ago, said: "I didn't find it easy.
"I made a bit of a run coming in and had a good putt on 16, but overall it wasn't too bad."
In finishing third Campbell missed an invitation to the Masters and also the prize for runner-up, which was entry into the final stage of international qualifying for the Open Championship in 2012.
Victory means a return to the Masters Tournament in April for Matsuyama, where he made history last year by becoming the first Asian golfer to win the Silver Cup for the lowest amateur score.
Runner-up was Soo-min Lee of South Korea.
Hamilton amateur Mathew Perry had a three-under 69 in the final round to climb to a tie for ninth place.
Vaughan McCall capped off a fine week in Singapore with a one-under 73 for a share of ninth, while Auckland's Ryan Fox had a disappointing four-over 76 to drop 10 places into a share of 17th.
International rookie Sam An, from the Titirangi Golf Club in Auckland, shot a three under 69 to finish also tied for 17th.