Dallaglio, who was ruled out of the tour after suffering an ankle injury in the opening match against Bay of Plenty, believes Woodward was not helped by a catalogue of crucial injuries.
"People look at the Tests as the main reason to go out there," he said.
"Everything else went very well apart from the Tests. We didn't just lose them, we lost them by convincing margins. I know Clive very well and he will be very disappointed but he will take the criticism and absorb most of it.
"We can look at the mistakes in terms of selection but right from the start things didn't go to plan. I wanted to make an impression but that lasted 25 minutes until I broke my ankle.
"I don't think the Lions lack enthusiasm and commitment but the difference was a bit of class. What's disappointing is that I think they are beatable when you put them under pressure, they react differently.
"It's easy to criticise but you have to look at the reasoning behind it. Where perhaps we did go wrong is the players didn't get to play enough.
"They all want to make an impression but only get a chance once every two weeks - that's how to gain momentum and get to know each other."