The Swans go into Sunday's Liberty Stadium clash with title-chasing Chelsea six points above 18th-placed Fulham with five games left.
After Chelsea, Swansea travel to Newcastle, then host Aston Villa before entertaining Southampton and visiting Sunderland on the final day.
"It's tight in the table around us, but we must concentrate on ourselves," Swans winger Dyer told the club's official website. "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 know what we have to do in the remaining five games. We have to keep plugging away and battling for everything.
"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."