Villa moved out of the bottom three courtesy of the goalless draw against the Gunners.
But Lambert refused to look upon the share of the spoils as a bonus point.
He said: "I wanted to win the game and we deserved something from the game.
"It's not always possible but we want to win every game we play.
"It can be regarded as a great point but I thought we were worth it, definitely, and we might have got something a bit more."