Neither side seriously threatened to break the deadlock. The midfield areas were relatively open but that did not translate to clearcut chances, with Hull keeper Allan McGregor making the only noteworthy save of the afternoon following Gabriel Agbonlahor's first-half run and shot.
Lambert highlighted the amount of time Villa spent on the ball but admitted that was not enough to warrant three points.
"I don't think either team did enough to win it, but from our point of view we had the lion's share of the ball," said the Scot.
"Someone has told me we had 75% of possession in the first half hour and for an away side in this league that is a vast amount.
"I never thought we'd lose it but equally I never really thought we'd win it.
"I didn't think either team really deserved (to win) it."
Villa sorely missed their star striker Christian Benteke, who is out with a hip problem.
Libor Kozak was a significant step down in quality in the centre-forward's role and Lambert must now hope Benteke does not come to further grief on international duty.
He has been called up by Belgium in spite of missing out here, but Lambert believes they are unlikely to be able to use him.
"We're obliged to let him go and Belgium have to assess him but I trust Christian to be honest," added Lambert.
"He'll know himself how he's feeling. At this time I wouldn't say he was fit."