Suarez scored four goals in Friday's CONMEBOL World Cup qualifier against Chile to highlight what has been an incredible rise in stature for Uruguay.
The 24-year-old played a key role in leading Uruguay to Copa America success in the summer and his latest performance for the national team brought out high praise from several quarters.
"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."
Suarez arrived at Liverpool from Ajax last January and has already established himself as one of the best players in the Premier League.
The Uruguayan is enjoying his football in England so much that he has indicated a desire to stay at Anfield beyond his current five-year contract.