Spagnolo enjoyed an eleven-year stint with the Scuderia, rising through the ranks and working directly with Kimi Raikkonen and Fernando Alonso while heading the Italian outfit's performance department.
"It's an area where we were deficient, if you like," Smedley told Autosport.
"We've already created a group around Antonio, and he's come in, he's got his own ideas, he's an extremely clever guy.
"He's definitely helping us already with what we've been able to do from Friday to Saturday, to find our feet and get ourselves back into what I think is a reasonable position for this year's Williams. He is playing an integral part in just helping us understand tyres."
Smedley explained that Spagnolo's expertise will not cure the Grove-based performance problems overnight but rather help the team "understand our competitors' strengths and identifying areas of our performance which require prioritisation of resources."
"There's a lot of other stuff we need to do, and in the background of R&D as well. It's not just about what we're doing on a weekend and the day-to-day survival.
"It's also about putting medium/long-term research and development in place that will bear fruit. It's to take us out of the performance field where we are now and on to the next level.
"It's not really just about trying to maximise what we've got, but looking where the next area of performance is. He will help us do that, along with his group, and we've got some good young people in there.
"We've identified talents around Williams and outside Williams, we're still actively recruiting and expanding.
"There's also a real long-term structure as to what we're doing with tyres, in terms of personnel and infrastructure and that's really the mentality the team has to have if we want to move forward."