The Potters climbed to eighth in the Barclays Premier League on Sunday as they held off Tottenham at the Britannia Stadium for a hard-fought - although highly controversial - third successive victory.
Coming amid a run of games that has also seen Tony Pulis' men qualify for the knockout stage of the Europa League, confidence has been restored after a tricky autumn spell, and Woodgate said: "It was a great win against a top team in Tottenham. They are going for the league title but it is hard to come to Stoke and get three points."
He added: "We are 11 men - a strong team. Nobody likes coming to Stoke. The referee doesn't like coming, the journalists don't like coming, the police don't like coming. Nobody likes coming to Stoke, apart from us."
Woodgate, one of four former Tottenham players to feature for Stoke during the game, impressed in his makeshift role at right-back as the hosts clung on for a 2-1 win.
Another Spurs old boy in Matthew Etherington also shone, the midfielder grabbing both Stoke goals in the first half after the visitors twice failed to deal with Ryan Shotton long throws.
Stoke survived a bombardment in the second half after Emmanuel Adebayor pulled Spurs back into the game from the penalty spot.
Spurs had two more penalty appeals turned down for handballs against Ryan Shawcross and Dean Whitehead while Adebayor had a legitimate-looking equaliser disallowed for offside.
And former England centre-back Woodgate, 31, is pleased to be enjoying his football again after being released by Spurs in the summer, adding: "I am delighted with every win, not just because it is against Tottenham. I want to win every game.
"I am happy with my fitness. That was my 12th or 13th game, which bodes well. I am playing football matches. That is all I wanted to do when I was younger. When you are injured it is not nice but when you start playing, you're fine again."
Source: PA
Source: PA