No rush to replace Winnall
Winnall, who hit 23 goals to finish as League Two's top scorer, completed a move to Oakwell for an undisclosed fee - which rumours suggest could hit £500,000 plus a percentage of any sell-on profit -on Wednesday.
That will leave Paddy Madden and Deon Burton as likely first-choice forwards for the Iron this term, with Lyle Taylor and youth team product Curtis Bateson to challenge them.
'We need to address the situation that Sam has left, but at this moment we will go with what we have,' Wilcox told the Scunthorpe Telegraph.
'It is early days in terms of looking for a replacement but I am having a talk with the chairman and we will go from there.
'There was interest form other clubs and Barnsley came back with a much-improved offer. Although we offered Sam a new deal he didn't take it.'
With centre-back David Mirfin ruled out for the start of the season, Wilcox's priority is to bring in an experienced defender to partner Niall Canavan.
Andrew Boyce, Callum Howe and Luke Waterfall have all been given a chance to stake a claim to play alongside Canavan during pre-season, but have yet to show they would be a suitable replacement come the season opener at Swindon next month.