Villa are five points above the Barclays Premier League drop zone heading into the home game with Sunderland on Sunday and are the lowest scorers in the division with 11 goals from 18 games.
They drew another blank on Boxing Day when losing 1-0 to Swansea but Lambert felt his side deserved at least a point at the Liberty Stadium and believes 13th placed Villa are on the right track to climb the table.
Lambert's two previous seasons in charge at Villa Park have seen the club finish too close to the relegation zone for comfort - five points on each occasion - but the Scot feels they "will be fine" when they start accepting their chances in front of goal.
"If we keep doing what we are doing and take the chances then we will win more games than not," Lambert said.
"There will be so many twists and turns throughout the season, but if we keep doing what we've been doing we will be fine.
"There are good players like Joe Cole still to come back and if we get everybody fit then we will certainly, the way we are playing, be a match for teams."
Christian Benteke has managed two goals in his last five games since returning from injury and suspension but Villa have still struggled to score in an eight-match sequence which has brought only two defeats.
They have scored more than once on only two occasions all season and top scorers Andreas Weimann and Gabriel Agbonlahor - who misses the Sunderland game after collecting a fifth booking of the season at Swansea - have a meagre three goals apiece.
Sunderland are one point and one place worse off than Villa following their 3-1 home defeat to Hull on Boxing Day and Lambert accepts that the two clubs cannot rely on tradition to remain in the top flight
"History tells you in years gone by you have to earn the right to stay in the league regardless how big your name is or how big the club is," Lambert said.
"Take out that top six big clubs and everybody fights like anything to stay in the league.
"Sunderland for some reason have been down there for the past few years but it doesn't matter how big the club is, it's earning the right to stay in it.
"They say get 40 points and see what happens
We have got 20 and last year it took us until January time to get 20, so that's an improvement."
Meanwhile, Sunderland head coach Gus Poyet has hit out at the Christmas fixture schedule as he attempts to rally his troops after a Boxing Day defeat.
The Black Cats headed into Friday's clash with Hull at the Stadium of Light riding the crest of a wave after their 1-0 derby victory at Newcastle, but succumbed in tepid fashion - despite taking a first-minute lead - to lose 3-1 to a side which had not won in 10 Barclays Premier League fixtures.
A stunned Poyet later admitted his team had simply not been good enough, but as he turned his attention to Sunday's trip to Villa, admitted he could not quite understand why he was having to do so.
The Uruguayan said: "One of the good things is that we play again in two days
That's the only good thing about playing today (Friday).
"We shouldn't be playing on the 28th
I've been in England for a long time and I know that Boxing Day games are a tradition and I accept that and think we should maintain it.
"But I think that then playing on the 28th is a disgrace
We shouldn't be playing then, we shouldn't.
"If you want to see the best players performing well, you need to make sure you are not playing every two days.
"It is not needed
That is not tradition and anyone who says it is is not telling the truth."
Poyet will welcome back striker Connor Wickham back from a one-match ban, although he was quick to dismiss any suggestion that the 21-year-old's absence against Hull had been a factor
He said: "I don't think that was the case
If so and he plays on Sunday, then we will win?"
Source : PA