The Uruguayan scored four times as the South American champions beat Chile 4-0 in Montevideo, leading pundits to draw comparisons between the 24-year-old and the Ballon d'Or-winning Argentinean superstar.
"Comparisons with Messi embarrass me," Suarez told El Pais. "It also makes me smile, but I feel the comparisons are just the reaction from the Uruguay fans as everything seems to be going well at the moment.
"I am happy, but we have to look at the work of the whole team as it is not just about one player."
Speaking after his performance against Chile, Suarez said; "You want to burst into tears, your stomach turns."
Suarez, who won the Player of the Tournament award in this summer's Copa America, has now scored 26 goals for his country, moving closer to the record of 32 held by team-mate Diego Forlan.
NEWSJoy for Suarez, irritation for Messi in qualifiers
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