The executive vice-chairman said the United board refused to sanction Mourinho's targets after taking advice.
Speaking to United We Stand (h/t Mark Critchley of the Independent), Woodward explained there had been a difference of opinion with the Portuguese.
"It is true that we didn't sign a centre-back in the summer of 2018 and it is true there was a difference of opinion on one or two players between the manager and the recruitment department.
"Sometimes I have to be one who delivers the 'no', which isn't easy. Our natural tendency is to back the manager in every possible circumstance. But we have to listen to the recruitment experts too."
United have restructured their recruitment after the failures of their past three managers. David Moyes, Louis van Gaal and Mourinho all struggled to integrate new recruits during their tenures at Old Trafford.
The Red Devils finally captured a centre-back last summer after the £80 million signing of Harry Maguire from Leicester City, strengthening the defence 12 months after Mourinho requested.
The recent arrivals of Aaron Wan-Bissaka and Daniel James under Ole Gunnar Solskjaer represented a shift in the type of big-name player United have previously targeted.
Woodward also told United We Stand (h/t Sky Sports' Tommaso Fiore) the club are conducting a review of development plans for their iconic stadium and training facilities.
"Our objectives for the stadium are for it to be safe, full and noisy. Adding more seats can influence the third one, but has to be done in the right way.
"There are no plans currently to increase capacity, but I'm not saying it can't happen long-term. If you totally change it then you can change the feel of it.
"We're looking at an investment plan while maintaining what makes Old Trafford special. Part of the allure of United or Old Trafford is the fact that it's a stadium that was built in 1910."
United remain one of the premier brands in world football, despite falling into decline on the pitch. However, most of their main domestic rivals have invested in their home grounds.
Manchester City and Liverpool have significantly redeveloped the Etihad Stadium and Anfield, respectively, while Arsenal and Tottenham Hotspur now occupy new world-class stadiums that rival any ground on the planet.
Rebuilding at United cannot just be focused on the squad, with the club's bricks and mortar also requiring an overhaul.