The Tigers take on Sheffield United at Wembley on April 13, but midfield man Meyler says the club need to start picking up points in their fight against the drop from the top flight.
Steve Bruce's side have won just two of their last 10 games and the 24-year-old Republic of Ireland international wants 13th-placed Hull to pick up victories from their next four matches.
They take on West Brom at the KC Stadium next before trips to West Ham and Stoke ahead of a home clash against Swansea prior to their first cup semi since 1930.
"It's a dream come true to be heading to Wembley to face Sheffield United for a place in the FA Cup final," he told reporters.
"The Premier League is our bread and butter, though, and I want to ply my trade at this level for the next five to 10 years, so securing our place in the top flight remains our priority.
"We need to kick on in the last 10 games of the season and secure our place in the top flight for next season as soon as possible.
"In the next few weeks we've got to play a lot of sides around us and we're hoping we can be safe before the semi-final.
"We're here to do a job and to push this club forward as a group."