The Reds lifted their first major trophy under Jurgen Klopp last term when they beat Tottenham Hotspur 2-0 in the Champions League final back in June.
The Merseyside outfit then followed that triumph up by beating Chelsea FC in the Uefa Super Cup in Istanbul last week to win another pieces of silverware.
Liverpool FC will have their sights firmly set on challenging for the Premier League title once again this season after they finished second and just a point behind champions Manchester City last term.
Oxlade-Chamberlain, 26, says he and his team-mates are keeping their feet on the ground but he feels that the stage is set for more trophies in the seasons to come.
Speaking in an interview with Liverpool FC’s website, Oxlade-Chamberlain said: “We’ve had a taste of winning [a trophy] and we knew what it took to get there.
“It was nowhere near easy. I think it’s going to get harder and harder.
“We know what it’s going to take, there are going to be moments that test us and maybe new tests this year that we didn’t face last year.
“We had to dig in, the boys dug in all last year through difficult moments, where you’re expected to win and still go out and win.
“We know there’s going to be tests and we know that’s what’s required.”
Oxlade-Chamberlain will be hoping to feature for Liverpool FC when the Reds take on his old side Arsenal at Anfield on Saturday evening.
Both the Gunners and the Reds are the only two teams in the Premier League to have won their opening two games this season.
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