On Monday, it was revealed that Wood, 25, who scored 30 goals for the Whites last season, had joined Premier League club Burnley on a four-year contract.
Radrizzani has revealed that Leeds did everything they could in a bid to keep the forward, but Wood's desire to leave Elland Road forced the Championship outfit into a sale.
"We offered the player strong financial terms including reasonable exit clauses, lower than the fee we demanded for a transfer this summer, should the club not reach the Premier League in a certain timeframe," read a statement from Radrizzani.
"However the player's preference was to leave Leeds United and as he only had one year left on his contract after this season we had to protect the club and ensure we did not sell Chris below our valuation.
"Supporters can rest assured that monies generated from the sale of Chris Wood will be reinvested into adding to the 12 signings we have made already."
Meanwhile, Leeds have revealed that any supporters with Wood's name and number on the back of their 2017-18 shirt are due an exchange.
"Following the departure of Chris Wood... Leeds United are advising any fans who have 'Wood 9' printed on the back of a 2017-18 home or away replica shirt that they are able to return the item to our club shop and exchange it for a new blank replica shirt," read the statement.
Leeds are currently fifth in the Championship table after collecting eight points from their opening four matches of the new season.