Yesterday's 1-1 home draw against Norwich means Lambert’s side have won only one of their opening nine Premier League games, leaving 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.”