The Villans were unable to capitalise on last week’s 2-1 victory over West Ham, their first win in eight games, as Santi Cazorla's late effort consigned them to defeat.
Lambert says his players also believe they will avoid the drop and has called on his side to repeat their recent performances if they are to stay up.
"The way they are playing, honestly, I can’t ask for any more," the Scot told reporters.
"Sometimes you walk off a pitch and think 'we didn’t deserve anything' but against Arsenal, I couldn’t be too disappointed with it.
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"We have belief in ourselves that we will always be okay. I don’t get caught up in the whole issue.
"The players believe [we can stay up too] because of the way they are playing. I’ve got no qualms about that whatsoever.
"They have been criticised in some quarters but they’ve never let their heads go down, they’ve always responded, which is great.
"They just need to keep going and keep that spirit and then hopefully win more games than not."