Just 26 games after lifting the trophy against Chelsea at Wembley, in which Woodgate scored the winning goal, manager Juande Ramos was sacked with Spurs rock bottom of the Premier League with just two points from eight games.
In stepped Harry Redknapp and despite an initial upturn in their fortunes the club still sit 14th in the table, just three points off the bottom three.
The 29-year-old has likened the situation to former club Newcastle where despite having the potential to succeed they too are struggling at the bottom.
Despite a disappointing season in the league, Spurs have the opportunity to secure silverware as they look to defend their Carling Cup crown when they face Manchester United in the final on Sunday.
"Maybe as a collective, we thought that winning the Carling Cup meant that we didn't have to push on," Woodgate said.
"We knew that we were in Europe and we didn't play good football in that spell. We can't let it happen this season.
"There's more pressure on us this year because of where we are in the table so we can't allow it to happen again.
"A lot of players seem to thrive under pressure so maybe we can show a bit of balls and do a better job this time."
SpringboardThe former Middlesbrough man insists that the club must now build on their cup run for next season and avoid a repeat of their shortcomings this term.
"I'm sick of people saying it to be honest," he added.
"We said the same things last season. You would like to think it would be a springboard with the manager we have and the players we have now.
"We're not showing that we can a top-five or six club. The potential is there but we always say that.
"It's a bit like Newcastle. They have a lot of talent as well."
With Sir Alex Ferguson already stating that he will stick with his youngsters for the final the England international is still expecting a tough game.
"The kids have that winning feeling as well, they will want to chalk up their first trophy and we saw how good their youngsters are earlier in the season," he said.
"They have the winning mentality drilled in to them and once they get one trophy under their belts they'll want a lot more."
VideoMeanwhile, Redknapp has been motivating his troops ahead of the final by putting together a video of past Spurs triumphs.
"We'll have a chat obviously. But we have got a little bit of motivational video that I like to show the lads," he said.
"It involves some of the Spurs team over the years winning cups and how great it was. We will show that with a bit of music to it and show how this particular team has scored some of the goals on the way to the final.
"It is all part of the deal. Our people have put it together, it is only about six minutes, but it is good."