The Cherries are underdogs going into a two-legged tie against the in-form Bees after finishing 10 points and three places below their opponents in the Sky Bet Championship table.
Yet the west London club travel to the Vitality Stadium on Monday evening holding a horrendous play-off record having failed to gain promotion on each of the nine prior occasions they have qualified, including an extra-time loss to local rivals Fulham in last season's final.
Woodgate feels Thomas Frank's squad will have been left with psychological scars from that painful setback but also acknowledges the disappointment could fuel their motivation for a return trip to Wembley.
"I wouldn't say the ones previous because a lot of the players weren't there for that but last season will have, definitely," Woodgate replied when asked if the opposition's past failures would have had a lasting mental impact.
"For me, they were one of the outstanding teams in the division. Last season they were exceptional and failed at the final hurdle.
"They've been to that final and lost and know what it feels like.
"It can work both ways; they know that feeling when they've been beaten in the final, they know how hard it's been for them. That can fester, that can stay in the minds of players.
"Both teams are under pressure. We know it's a pressurised situation. We know it's an absolute monster game and the players know that.
"They are the favourites to go up, there's no question about that."
Bournemouth are bidding to bounce back to the Premier League at the first time of asking following last year's relegation, while Brentford are seeking to end a 74-year absence from the top flight.
Woodgate unexpectedly stepped into the Cherries hot-seat to replace the sacked Jason Tindall in early February just days after arriving at the club as a coach.
The former Leeds, Newcastle, Real Madrid and England defender regularly performed on the biggest stage during his playing career but insists the responsibility of management is a "totally different ball game".
"This is huge and when you are the manager, the buck stops with you," he said.
"You are the one who puts the tactics together and looks to implement the game plan on to the opposition.
"It's a pressure that I like, it's a pressure I really enjoy. I wouldn't be here if I didn't like pressure.
"I think the pressures are totally different from being a manager to being a player. It's a totally different ball game."
Woodgate's existing Bournemouth contract runs until the summer and he repeatedly dodged questions about his longer-term future.
While Brentford – who host the return game on Saturday – are 12 games unbeaten, his side ended the regular season with three successive defeats without scoring, a run which began with a 1-0 defeat to the Bees on April 24.
The 41-year-old is unconcerned by the untimely wobble and backing his players to get the job done.
"Sometimes you have a small blip but the players are focused," he said.
"We know on the big stage the players should be there and I am sure they will be; we've got some outstanding individual talent in that changing room and we all need to turn up and do what we can do.
"I wouldn't change any of my players for theirs, I love the squad that I've got.
"The players have been in these situations before where they play in big games and we have got some really big players in that dressing room who hopefully deliver the goods for us."