Villa looked like they had earned a point before Santi Cazorla's winner.
Lambert was disappointed to see his team come away with nothing despite a pleasing display.
"We shouldn't have lost it," the Scot said. "We were exceptional in parts of that game and we should have been in the lead at half-time.
"At the very least we should have come away with a point. We've played like that for a number of weeks: West Brom, Everton, Newcastle in the second half, West Ham.
"We've just got to try and get more points on the board. We've got massive games still to come, and there'll be a lot of twists and turns this season."