Villa dropped into the bottom three with a 1-0 home defeat to Southampton, a result that followed a 3-1 reversal to League Two side Bradford City in the first leg of the Capital One Cup semi-final.
Lambert's side were widely booed off on Saturday but the manager, who is understood to retain the backing of owner Randy Lerner, is confident he can inspire an upturn.
"You can't panic," Lambert told the club's official website. "You keep going. There's a long, long way to go. There will be loads of twists and turns.
"If you look at the middle of that table, there is not much in it. There are about eight or nine teams.
"I do (expect Villa to climb the table). I said that from day one. I just do."
Villa have picked up just one point in five league matches but Lambert insisted defeats to fellow strugglers Wigan, as well as Southampton, did not heighten the pressure.
"It doesn't matter if it's Southampton, Wigan, Liverpool or Manchester United," he added.
"I never take any game lightly. I think every game in this division is tough."