Since beating Chelsea last month, the Midlands outfit have lost four games in a row.
Their latest fixture on Saturday resulted in a 1-0 loss to relegation battlers Crystal Palace.
"We're going to stick together," Guzan told the club's official website. "There are a lot of points to play for. We know the fans are disappointed, as are we. Everyone at the club is desperate for a win to end this run of defeats.
"For us as players and as a club we have to keep fighting and we're definitely going to do that. We all help each other. It is not the first time we've had a bump in a road and it won't be the last.
"That is part of being a professional footballer. We have to continue to fight and we will do that. We'd love to turn it around next week."
Villa, who are four points above the relegation zone in the table, will take on Southampton on Saturday.