Under Jurgen Klopp, the Reds this season ended their 30-year for the Premier League title, adding to the Champions League triumph in the previous campaign.
And Oxlade-Chamberlain says the team want to build their own legacy and inspire future generations at Anfield.
"You can't take moments and nights like this for granted," Oxlade-Chamberlain told the club's website. "You can't take playing for an amazing football club like this with fans that care so much, you can't take that for granted.
"So, as a player you need to seize those sorts of moments. We are here for a short time. We have our little spells, hopefully making history at this football club, we've got to do our bit to inspire the next generation like Steven Gerrard inspired me.
"At the minute we are going that way to doing that, but we need to go on now and have a strong streak for a few years and once said and done, that will be our story told and this football club will go on and hopefully people can follow us too, but we've got more work to do here and it's an amazing start to a journey.
"We've done really well in the last three years since I've been here and we need to just keep building on it, but it's a good time to be a Liverpool player and to be involved in this amazing football club so I'm really looking forward to what comes next, but we need to stay hungry and stay focused."
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