Former Leeds defender Woodgate kept news of the death of his father Alan, to himself, and opted to play as Boro opened with a 2-1 loss to Leicester City.
“Having had a close relative pass away when I was playing, you want to keep going,” said Mowbray, who has granted Woodgate leave ahead of tonight’s game.
“I gave him the option (on Saturday) but he wanted to get his boots on and go out there and he did exceptionally well for us.”
Mowbray has welcomed the distraction of the Capital One Cup after the season began on a disappointing note.
“The season’s about your league form but we saw last season that victories in this competition were part of some good for us,” he said ahead of the visit of Accrington Stanley, in the first-ever meeting of the two teams.
“They’ve got experienced players such as Nicky Hunt and Danny Webber. They lost 4-1 at Newport County and I’m sure they’ll have had a few words and want a reaction.
“They’ll be a very honest and hardworking side, fully committed to the game. They’ll want to win a game as quickly as they can and this is a shot for nothing for them really.
“We have to guard against any lack of application and make sure we do our job. We had some tough matches last time and we’re not taking anything for granted against Accrington.”
Defender Frazer Richardson, who last week signed a one-year contract last week, will not be involved, but Mowbray does not plan on making wholesale changes.
Last six games: Middlesbrough LWLDLL; Accrington DDWWLL.
Referee: S Duncan (Northumberland).
Last time: Never met.