Despite dominating possession for much of the game, the hosts could not find a breakthrough against a tenacious Crystal Palace defence.
Christian Benteke and Alan Hutton both wasted good opportunities as Villa failed to find the net for the 11th time this season in the Premier League.
"It was frustrating because we never took our chances," Lambert told BBC Sport. "We looked comfortable with a lot of possession.
"We have lost two of the last 10 but we would like some more wins in there. In all credit to them we kept on going but we could have got a goal or two."
Lambert also felt Palace, who look set to confirm Alan Pardew as their new boss this week, deserved praise for arriving at Villa Park with a clear plan to stifle the hosts.
"You have to give Palace credit because they got everyone behind the ball and sat deep and kept it tight," the Scot added. "We had creativity there but never took our chances.
"I remember playing here last year against Palace and got hit by a sucker punch and we didn't want that to happen again. You don't want players to pass for the sake of passing. We have started something new and we just need to finish it off."
Villa's poor goalscoring form could see them dip into the transfer market in January, with Lambert refusing to rule out the possibility of bringing in new recruits.
He added: "I need to speak with the chairman and the chief executive. If we can do something and it is right for the club financially I am sure we will."
