Villa have lost four games in succession to languish in 14th position on 34 points, just four points clear of the relegation zone with five games remaining.The Birmingham outfit have conceded 11 goals in that period, which has led to calls for manager Paul Lambert to be sacked.
But Guzan says the Villa players are sticking together as they look to return to winning ways against Southampton at Villa Park on Saturday.
"We know the fans are disappointed, as are we," said the United States international.
"Everyone at the club is desperate for a win and to end this run of defeats.
"For us as players and as a club we have to keep fighting and we are definitely going to do that.
"We have to continue to fight and look to turn it around next game."
Villa's poor run of results has coincided with Christian Benteke's season-ending injury.
The Belgian international, the club's leading goalscorer with 10 goals, was ruled out of the upcoming World Cup after rupturing his Achilles tendon in training earlier this month.
Midfielder Leandro Bacuna (five) is the only other Villa player to have scored five or more goals this season and Guzan knows the attacking trio of Gabriel Agbonlahor (three), Grant Holt (one) and Andreas Weimann (three) must help ease the load in the absence of Benteke.
"We lacked that little bit of a cutting edge. But we are going to stick together, there are a lot of points to play for," Guzan said.
"We all help each other. It is not the first time we have had a bump in the road and it won't be the last."
Villa, who have never been relegated from the Premier League since its inception in 1992, face Swansea, Hull, Manchester City and Tottenham in their remaining fixtures.
