And the left-back thinks Ole Gunnar Solskjaer’s first match went so successfully because United were more purposeful with their passing and took their chances.
The Red Devils thrashed Cardiff 5-1 with a rampant attacking display having failed to score five times in a single match in 144 games under predecessor Mourinho.
The Portuguese tactician was axed after United had won just seven of their first 17 Premier League games and lost five, including a meek reverse at the hands of bitter rivals Liverpool days before Mourinho’s sacking.
Yet the 55-year-old – who had a won league title in all of his previous five jobs – led United to the Carabao Cup and the Europa League in his first campaign having also beaten Leicester City in the Community Shield.
United also reached the FA Cup final in his second season, although they lose to Mourinho’s former club Chelsea.
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And defender Shaw, despite having a rocky relationship with the world-renowned coach, insists Mourinho should still be respected because of the trophies he won at Old Trafford.
That is in spite of United having been 19 points off the Premier League summit and 11 off the top four at the time of his departure.
Shaw told reporters: “It’s not very nice when something as big as that happens at the club but I think we all as players and as a team show respect in what happened.
“People might be quick to forget what Jose did for United – the three trophies he won – he did a lot. Obviously, one of the trophies was one we had not won before.
“He took us to three trophies in one season so those people need to respect him and remember what he did for not only us as a team to win those trophies but the fans as well.”
The win at Cardiff has helped trimmed United’s gap to the Champions League spots to eight points and injected some much-needed belief and confidence among both players and supporters.
And on the main differences of their first game under Norwegian club legend Solskjaer, Shaw thinks their work on the ball was much improved but also felt they were simply more clinical than recent months.
England international Shaw added: “We moved the ball quicker. The goals we scored were magnificent.
“Under any manager or any circumstances that’s how Man United are expected to play.
“I think in games before we have had a lot of chances that maybe could have ended up in the back of the net, but we didn’t take our chances.
“Thankfully, today, we did and it was nice to get the five goals we haven’t done for a while and we push on from there.”
United face relegation-threatened Huddersfield in Solskjaer’s first game in charge at Old Trafford – where they have won only five of their 12 games in all competitions this term – on Boxing Day (3pm).