Garry Monk's men sit 15th in the Premier League table, six points clear of the bottom three, but have won only once in their last eight Premier League games.
With five matches remaining, the Welsh club are looking nervously over their shoulder at the relegation zone, and winger Dyer called on his team-mates to show the spirit needed to pull away from danger.
"We know what we have to do in the remaining five games," he told Swansea's official website. "We have to keep plugging away and battling for everything.
"It's tight in the table around us, but we must concentrate on ourselves. It's in our hands so we must take our opportunity.
"Of course, you do have a look to see how the other teams have got on, but we don't get too high or low with those outcomes.
"We don't look at it as though we are doing enough to finish 17th. We want to get as many points as possible to finish as high up the table as we can.
"We are all pushing each other on in training. Every squad member has to do their bit whether they have been in or out of the squad, and that attitude has been evident on the training ground."
