Leeds were unable to extend their winning streak to eight matches on Monday night after being held to a goalless draw by Liverpool at Elland Road. David O'Leary's side now find themselves six points adrift of the leaders, Manchester United, with only six games left to play - but Woodgate is refusing to throw in the towel.
Such confidence is borne out of the infectious enthusiasm which has been generated by Radebe, Woodgate's central defensive partner.
The South African international, who turned 30 yesterday and celebrated the occasion with the man of the match award, faced Liverpool just over 48 hours after playing for his country against Gabon in an African Nations' Cup tie.
And Woodgate believes that when a player shows such dedication to duty, it is easy to see why it should rub off on those around him. "Lucas Radebe was outstanding," Woodgate admitted. "He's a great player to play alongside because he makes it so easy for you.
"I learn from him every single day, not only about football but in other ways as he's always happy around the place. He's excellent in training and he shows what an outstanding player he is on the pitch, but he's always got a smile on his face.
"He's a jolly person who helps pick you up when you're having a down moment - but he can also give you a rollocking as well."
So with matches at home to Alex Ferguson's side and fellow title challengers Arsenal and Chelsea still to come, the 19-year-old Woodgate is confident Leeds are not out of the championship running yet.
"I don't think it was too much to expect for us to keep the winning run going," revealed Woodgate. "That's the way it goes in football. You can't win every one.
"But the main thing is we didn't get beaten and so are still unbeaten in the League since early February.
"Hopefully, we can still challenge for the title - we're at least going to have a big say in it - I'd like to think we are still in with a chance.
"We are a young, confident side, so we are going to be and think like that. Now we can't wait for the big teams. We play better when they are at Elland Road. We rise to the occasion."
Leeds' Norwegian international Gunnar Halle will undergo a second scan today on the left knee he injured during the first half of Monday night's game.
An initial ultrasound scan yesterday appears to have confirmed there is no ligament damage. However, the specialist has told the 33-year-old to also have an MRI scan to make absolutely certain.