United enter the weekend third in the standings and 11 points behind Arsenal, albeit with a game in hand on Mikel Arteta’s leaders.
A first Premier League title in a decade looks a big ask with 14 matches to play, with Shaw and co heading to Merseyside knowing they need a first Anfield win since 2016.
“They’re always big, big games,” the long-serving United left-back said. “I think if we want to be challenging for the title, I think we need to be going there and winning these games.
“But, of course, on the other hand, we know it’s going to be an extremely tough game.
“They’re always a tough game against Liverpool. They’re an amazing side, a really good side and I think it’s going to be a good game.”
Shaw said “it’s a bit silly” to talk a potential quadruple at this stage, but the fact it is even a possibility underlines the impressive work done by manager Ten Hag.
Appointed with the Old Trafford giants at a low ebb last summer, the Dutchman has overseen a marked change in fortunes and led the club to a first trophy since 2017 against Newcastle.
“I think all of us can look at it as a fresh start,” Shaw told Premier League Productions.
“It’s been a tough sort of few years here at United and I think, yeah, it can be a new beginning.
“We spoke about before the (Newcastle) game it’s a new era, it’s time to sort of create our own history with a new manager, with new players, new team. I think it was a great start in the direction we want to go in.”
Sunday was a special moment for Shaw, who ended his long wait to a trophy as part of the matchday squad having joined United in 2014.
The 27-year-old has developed into an integral figure under Ten Hag, who had dropped him and captain Harry Maguire after United lost their first two matches of the season.
“I think he’s obviously changed everything,” Shaw said. “The culture in the club, you know his strict rules, the way he wants to play, his tactical points on where he wants players to play.
“He’s changed everything – but he’s changed everything for the better.
“After a tough start of the season, he’s transformed this club into where we should be.
“He’s extremely strict, but I think he knows how to win and he knows how to get the best out of the players. I think especially after, like I said, the start of the season he changed everything, and I think changed it for the better.
“We’re in a really good place now and the confidence and belief is definitely building more and more but I think we have to take it game by game.”
Ten Hag expects Shaw to be fit for Sunday’s match after missing the midweek FA Cup comeback win against West Ham with a knock.
United showed their fighting spirit to come from behind to win that fifth-round clash, just as they did when doing so the previous week against Barcelona in the Europa League.
Their mental strength was vital in those victories and their Carabao Cup triumph, with summer signings Casemiro, Lisandro Martinez and Antony helping foster that winning mindset.
“It’s easy to see,” Shaw added. “I think it always helps when you add quality players in that have won trophies before and have got that experience of knowing how to win big games and big finals.
“I think we saw that (Sunday) night in the game with obviously an amazing performance from Case with his experience.”