Aside from a 10-week spell immediately following Ole Gunnar Solskjaer's appointment as United manager in December, when the Red Devils won 14 of 17 matches in all competitions, the 2018-19 campaign was about as disappointing as possible for the Manchester giants.
Not only did they finish sixth in the Premier League behind all their main rivals, meaning they won't appear in the UEFA Champions League next season, but local foes Manchester City won a domestic treble.
Per James Robson in the Evening Standard, Shaw said "none of us want that to happen again" in 2019-20, and he explained how Solskjaer has been preparing United for the new campaign with pre-season victories over Perth Glory, Leeds United and Inter Milan:
"It will be a new United this season, especially with the new ideas the manager is bringing in. The manager said last season what he wanted from us and he wanted to work us hard and get his ideas in. This pre-season has been really tough for everyone, physically and, at times, so hard mentally. But it is helping the squad massively.
"I feel we looked a lot better [against Inter] than we probably have for a while. Ole is more focussed on keeping the ball, playing out from the back and keeping possession. A lot of times last season we didn't do that well enough.
"We've worked a lot on tactics, pressing-wise. When to go, what sort of moments. The other side of that is to keep the ball. Just to keep the ball more and play as a big team, a good team. We want to be winning games, but with possession as well. He's made his ideas clear."
Shaw added City and Liverpool "won't have it as easy" in 2019-20 as they did last term, when they were in a different class to the rest of the Premier League:
United's first aim next term must be to return to the top four after a run of five winless Premier League games to close out 2018-19 scuppered their chances of securing Champions League football.
The Red Devils face one of their top-six rivals on the opening day of the 2019-20 season when they host Chelsea at Old Trafford on August 11.
Picking up a victory against the Blues could be crucial to United starting the season well, as it would give them a big boost going into another tough game against Wolverhampton Wanderers a week later.
Wolves finished seventh in the Premier League last term, and were unbeaten in three fixtures against United, earning 2-1 victories at home in the league and FA Cup, and earning a 1-1 draw at Old Trafford.
In order to make gains on the top four and give any indication they can be title challengers again soon, United have to reverse those kind of results in 2019-20.