Saturday's 1-1 home draw against Norwich means Lambert's side have won only one of their opening nine Barclays Premier League games, and left them hovering just above the relegation zone.
Michael Turner's late equaliser denied the Scot victory against his former club after Christian Benteke's opener and the sending-off of Villa left-back Joe Bennett for two bookable offences.
It needed three fine saves from Brad Guzan to ensure the hosts a point.
But Lambert is confident Villa will retain their top-flight status as he rebuilds the team ahead of testing games with Sunderland, the two Manchester clubs and Arsenal during the next month.
Lambert said: "I know the stats. We have to try to win games.
"But I have a real faith and trust in these players. I have great belief in them. I'll stick with them. They will be fine.
"I've not been long here and we just need to keep building and building and keep doing our best.
"In terms of the league, there is nothing in it (points-wise). If the lads keep the effort and commitment going, then they will be fine.
"The character we show is a major plus every game.
"The team battled brilliantly against Norwich not to get beat after the sending-off of Joe, which is a great trait to have.
"If you can't win the game, then make sure you don't lose it. Some of the defending was exceptional."
Guzan has fully justified Lambert's decision to replace the vastly experienced Shay Given with the United States international.
He left Villa at the end of last season but was persuaded to sign a new three-year deal after Lambert's arrival as Alex McLeish's successor.
Lambert said: "Brad is in world-class form at the minute. He's a really top, top goalkeeper.
"I think the football club is fortunate to have two world-class goalkeepers at the moment."
Chris Herd helped Villa overcome the absence of three centre-backs through injury with an assured performance.
But Lambert will be without winger Charles N'Zogbia for the foreseeable future after he suffered a knee setback in training.
"Charles hurt his knee in training on Thursday and we think he'll be out for a few weeks," the Villa boss confirmed.
Four points from the last two games have eased Norwich's relegation fears, meanwhile, and their fans chanted manager Chris Hughton's name rather than directing verbal abuse towards Lambert.
Hughton said: "Any chanting towards me is a reflection of what they see on the football pitch.
"They are certainly not going to chant my name if they don't like what they see on the pitch.
"I think they've enjoyed what they've seen in the last couple of games.
"I think we played well enough over the 90 minutes against Villa not to lose the game, so the draw for me was almost a starting point.
"On another occasion, with the possession and chances we had, you get a bit of fortune or show that bit of quality and you win the game."
Wes Hoolahan was the most creative player on either side and fittingly set up the equaliser for Turner.
"Wes is a player you want to get on the ball," Hughton said. "Playing him off the front man, you can get him into more advanced positions.
"But equally, if you play him a little deeper, you know he can influence the game from there."