"I hit him well in the first round but it's hard to fight a guy who doesn't want to fight," he added.
The 27-year-old was cut early in the fight with a left hook by Strickland.
This was Duddy's last contest in the United States before he comes home to Ireland where he has already signed up for two bouts, the first scheduled for the National Stadium in Dublin on 14 July.
An opponent for the Dublin bout has yet to be named although Jim Rock is being mentioned in some quarters.
Highlights of John Duddy's latest win will be on BBC One Northern Ireland on Sunday evening (20 May) at 2220 BST