Bradley Dack’s header gave the Championship side the lead at St. James’ Park, but Matt Ritchie’s late penalty levelled matters for the hosts.
The 1-1 draw means United will head to Ewood Park for a replay to decide who goes through to the fourth round.
And Woodman – who made his first start of the season against Rovers – says while the Magpies were frustrated not to have secured their place in the next round after 90 minutes, they must look on the bright side as they remain in the hat.
“As a team it’s disappointing – we wanted to win the game – but at the end of the day, we’re still in the Cup,” the 21-year-old told nufc.co.uk. “We’ve got another game which isn’t ideal but for me on a personal note, it could be another chance to play.
“There are mixed emotions really – we wanted to win the game, but we’ve got to look on the positive side. We’re still in the cup, so that’s good.
“One thing about this team is you can never question the desire to win and the work rate. Everyone out there wanted to be there, and wanted to win. Sometimes it doesn’t happen and you have to take a draw.
“But we’re still in the Cup, and it’s a good opportunity now to go down there and hopefully progress in the tournament.”
Woodman made his senior United bow at the same stage of last term’s FA Cup, starting the victory over Luton Town.
The England Under-21 international – who lifted the Under-20 World Cup with England in 2017 – felt he acquitted himself well against Tony Mowbray’s men.
“There were a lot of crosses, a lot of argy-bargy in the box and things like that, but I thought the team reacted well after going a goal down,” he said. “Matty tucked away his penalty and after that we looked to try and push and get a result. It wasn’t meant to be, so we’ll have to go down to Ewood Park and get a result there.
“I felt like I was solid. I just tried to do the basics right, and I felt I got that right. I got a lot of crosses from (Charlie) Mulgrew and that was difficult but on the whole, I felt like I did well. I will watch it back tomorrow morning in more depth but, just coming away from the game now, I felt like it was a decent outing.
“My old mate Arma (Adam Armstrong) was pulling my shirt and doing all sorts of little tricks and that, but it’s part of the game. It’s just about how we deal with it, and I felt that as a team we dealt with that well.”
The replay against Rovers could present Woodman – who has provided backup for regular number one Martin Dúbravka in recent weeks – with another opportunity to show what he can do.
“It’s just about keeping my mind focussed. I go into training every day with a purpose – to try and get better every day,” he explained.
“I’ve done that since I was a kid and I’ll continue to do that whatever happens. It’s all positive – it (the replay) does give me an incentive to keep training hard and working hard, and to keep trying to improve.”
