"We needed to freshen things up in the close season so that we can kick on next term, and I'm confident that we can do that," Carey told BBC Sport.
"We haven't got a lot to spend, but if players become available we will continue to recruit."
Carey says Williams can solve Wrexham's goal-scoring woes from last season.
"We struggled up front, but Eifion is one of the better players in the division and a very experienced man at this level," Carey told BBC Sport Wales.
"I've had to face him and I know what he's like. He's also very versatile and played a lot in midfield for Hartlepool."