The Reds secured their first honour since the League Cup in 2012 when they won the UEFA Champions League last season.
Oxlade-Chamberlain is under no illusions as to the difficulty the Reds face in winning more silverware, per Glenn Price for Liverpool's official website:
"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."
Last season's Champions League win came after heartbreak for Liverpool in the final of the same competition in 2018, as well as in the 2016 UEFA Europa League final.
As well as winning the Champions League last season, Liverpool finished second in the Premier League by one point, having racked up 97.
Jurgen Klopp's side started this season with the possibility of winning seven honours: the Community Shield, UEFA Super Cup, FIFA Club World Cup, Champions League, FA Cup, Carabao Cup and Premier League.
The Guardian's Sachin Nakrani observed Liverpool's need to dig in to beat the Blues:
Liverpool writer Dave O'Connell is pleased Klopp has been able to instil a winning mentality in the squad:
The Reds will be favourites to win the Club World Cup too. The European representatives have won the tournament every year since 2007, with the exception of 2012.
They're also capable of challenging for any of the other trophies available. Their focus will be on the Premier League and Champions League, though, so the domestic cup competitions may fall by the wayside as they did last season, in which they exited both in the third round.
Winning major trophies consistently is difficult even for teams of Liverpool's calibre, but it's clear from Oxlade-Chamberlain's comments that he and the squad recognise as much.