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.
Looking ahead to testing games against 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."
He went on: "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.
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.
"The character we show is a major plus every game," Lambert added. "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."