It was a difficult return to Elland Road for the former Whites centre-half but he was gracious in defeat, praising Marcelo Bielsa and his victorious side, who went top of the Championship again at full-time.
He also had praise for the effort levels and desire of his own struggling team.
"Leeds are a really, really good team, the best team in the Championmship without doubt," said Woodgate.
"The lads kept on going to the end, working as hard as they can. Positives, there were eight academy players in the matchday squad. It's disappointing, you don't like to get beat but they're a good team. Poor [second] goal to concede, a killer, 20 seconds to go in the half, poor defending.
"When you're 2-0 down going into half-time it is difficult to get back into the game. They gave me everything they had. The squad's really thin. They wanted to give everything.
"We need to win our home games and see what we can do when we go away from home. Maybe a West Brom are as good as that. We've got to remain positive. I can't knock their effort. Leeds are a top team, coached by a top, top manager. No excuses, we got beat by a better team."
When discussing the difficultly of the challenge faced by his Boro players today, Woodgate pointed to the stark contrast between the strengthening Leeds have done since last season and the situation at the Riverside.
"They've improved their squad massively, you've got Patrick Bamford firing on all cylinders, [Eddie] bringing Nketiah on, he's a really good player, you've got Ben White on loan from Brighton. We've lost a lot of players and replaced them with three younger players from League One.
"These young lads are just finding their way in the game. It's not fair to them for me to do it but needs must at this time. We need to do business in January."
Woodgate was seen in conversation with Bielsa at full-time on the touchline but wouldn't be drawn on what was said between them, simply calling the Argentine a 'really good manager and a really nice man.'
He was, however, happy to put on record his appreciation for the continued support of the travelling Middlesbrough fanbase and for the reception he received from the Leeds supporters.
He predicts they'll enjoy a bright future, should United return to the top flight.
"The [Boro] fans have been really good to me. Still staying to the end and still applauding. The fans will stick by us.
"[The Leeds fans were] unbelievable. I couldn't clap them at the time, we're getting beat. A top club, I wish them all the best.
"If they get in the Premier League it'll be some train to get on, it'll only go one way. I've been there. It's an incredible club."