Villa dropped into the bottom three of the Barclays Premier League after Saturday's 1-0 home reversal against Southampton but Clark is confident Villa can escape from their current predicament - especially when players like captain Ron Vlaar return to the side after injury.
Clark said: "Are the players still fully behind Lambert? Definitely."
Saturday's defeat came after a controversial penalty was converted by Rickie Lambert, and Clark continued: "Our luck is out at the minute as you saw with the penalty given against us which was not a penalty.
"In the next few weeks hopefully it will turn and we'll get a bit of luck and maybe put three or four goals past a team.
"We need to keep our heads up. We have West Brom to come next weekend and we need to stay positive and look forward to that.
"After the game, heads are down, but in the next couple of days we'll pick ourselves up in training and we'll get back together.
"We'll stick together, we are a close team and we'll look forward to the next game. There are enough characters, there's definitely enough togetherness between us all.
"Over the next few weeks it's important for us to pick up some points and, if we stick together, I'm sure we'll be able to do that."