The Reds have made an excellent start to the season and suffered only their second defeat of the campaign when they lost to leaders Arsenal at the weekend.
Suarez, though, believes that Liverpool's unexpected title charge can continue in the coming months.
"The expectation is huge," Suarez told French radio station RMC.
"This season we started well, with the desire and hope. We do not have to compete in the European Cup which allows us to concentrate 100 per cent on the championship.
"The Premier League is very tight this season and anything can happen against anyone."
Suarez's burgeoning partnership with Daniel Sturridge has continued following his return from suspension and a summer of speculation after he demanded a move away from the club.
But the Uruguayan insists he is now settled fully back into life at Anfield.
"When I was separated (from the squad), the players told me they didn't like that and wanted me to be with the group," he said.
"Today I feel very supported by my team-mates, and I appreciate their support.
"The support of the fans was also very important. I always could walk on the street with no trouble. I was never threatened or anything like that - the people told me to stay.
"I feel part of things at Liverpool. It is my home. I am comfortable and happy here - I work hard for Liverpool and I will always be thankful to the club, and to my team-mates."