The stands at Lima's Estadio Nacional will be empty after Peru were punished by FIFA for crowd trouble at their previous home qualifier last month when fans threw objects at Argentine referee Patricio Loustau after a 2-1 defeat by Uruguay.
"This is the last (qualifying) match and we're going to play as if it were the most important," Markarian told a news conference. "It's surely my last match with the national team, I feel great sadness at leaving this job."
The highlight of the 68-year-old Uruguayan's three years in charge was third place at the 2011 Copa America in Argentina but during his time in the job he failed to end Peru's World Cup qualification drought dating back to 1982.
"I leave with more players consolidated (in the Peru team) than I found," Markarian said.
"We have definitely built a squad for the future ... the directors backed me all the time. I tried to do my best but it wasn't enough."
Markarian, whose team have won four and lost nine of their 15 qualifiers, gave a qualifying debut to teenager Cristian Benavente on Friday when Peru lost 3-1 to South American group winners Argentina in Buenos Aires and is excepted to give him his first start on Tuesday.
"We're looking to change Peruvian football's image. We must find solutions to face the next qualifiers (for the 2018 World Cup) successfully," midfielder Benavente, who is on Real Madrid's books, told reporters.
Peru have produced many skilled players over the years, from Teofilo Cubillas, who inspired them to the World Cup quarter-finals in 1970, to Paolo Guerrero, top scorer at the 2011 Copa America.
They have been let down by poor organisation, indiscipline and the failure of players to become more tactically aware.
Markarian earned his appointment in 2010 after several years in Peru coaching club sides Universitario and Sporting Cristal and winning the league title with both in the 1990s. He has also coached in Paraguay, Greece, Mexico and Chile.
- Sports & Recreation