A traumatic night at Franklin's Gardens saw the Saints' whitewash breached six times and the try-scoring bonus point conceded by the 37th minute.
Wood gave an honest assessment of a night that director of rugby Jim Mallinder viewed as the low point of his six-year reign in the east midlands.
"There was no hairdryer treatment after the match because we're all pretty ashamed," the England flanker said.
"To have fans call you an embarrassment as you leave the field is about as bad as it gets.
"All we try to do is make the fans proud but we can't be proud of what we did out there and we can't expect them to be. We can only apologise for that.
"I'm ashamed and embarrassed and collectively the team are too.
"It went wrong everywhere. We were like an unopposed team for much of the game.
"Leinster have a great track record and a great European pedigree, but they're not 33 points better than us. We just didn't turn up, I don't know what's wrong with us.
"It should never have got to that stage because these are the occasions you live for in rugby.
"It's one thing to lose to a better side, but to lose having not even played a hand is soul-destroying. It was unforgivable.
"It felt like they had twice as many players as us and you didn't know what hole to plug first.
"That's probably the longest 80 minutes I've ever played and I'm ashamed to say it but I couldn't wait for the final whistle."
Leinster host the second instalment of the double-header at the Aviva Stadium in Dublin on Saturday having opened up a five-point lead at the summit of Pool One, with Northampton in third.
Saints must produce a bonus-point victory to have any hope of winning a group that also includes French champions Castres and the Ospreys.
"We've been given yet another hard lesson. We have to front up, take a long hard look at ourselves and show Leinster the real Northampton next weekend because that was unrecognisable out there," Wood said.
"We'd like to salvage some pride, that's not beyond us. There may be some complacency from them after they destroyed us at home.
"Hopefully we can put in a performance we'll be proud of. It's a dire situation because we had a real chance."