Villa were beaten by Championship side Millwall 2-1 at The Den on Friday night and were also dumped out of the Capital One Cup at the semi-final stage by Bradford.
Paul Lambert's side are also perilously close to the Premier League relegation zone, with Villa just one place and one point above 18th-placed Reading.
Villa face fellow strugglers Newcastle in the Premier League on Tuesday but Austria international Weimann, who is in talks to extend his contract at Villa Park, insists they can secure their top-flight status if they remain positive.
"If you don't believe (you can turn it around) there is no point playing," he said.
"A month or so ago we beat Liverpool and Norwich and then it turned. We have got to stick together as a team now things are not going well.
"We have got to learn to hold on to leads. It is a massive game for us on Tuesday night and hopefully we can start winning from there.
"It is going to be a tight game and we need to see it through, score a goal and win the game. The fans have been outstanding and hopefully we can get a few wins mainly for them."
Both goals conceded in the cup defeat to Millwall came from crosses and Weimann echoed his manager in demanding they tighten up in defence.
"Obviously everyone is disappointed because we started off well and got the goal but then conceded from a set-piece," he added.
"We need to get a win soon. When you can't win the game you say don't lose it, but unfortunately it was another cross that we couldn't defend and they scored."
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