A remarkable, chaotic, mesmerising Premier League thriller at Old Trafford captured the imagination even of the clinical operators in the dugout. "Really difficult to explain," said Bournemouth manager Andoni Iraola. "But I prefer 4-4 to 0-0."

"Fun," was Manchester United counterpart Ruben Amorim's initial observation. Analysing for Sky Sports, Jamie Carragher went further. "The best game of the Premier League season so far," said the former England and Liverpool defender. "It was almost a throwback to Alex Ferguson's Manchester United with attacking football.

"It is the best I have seen Man Utd. For the majority of the game, they were absolutely fantastic. For the first time under Amorim - and first time in a long time - I felt like I was watching what Man Utd are supposed to be. Wave after wave attack, but the inability to defend has hurt them."

For the record, Ferguson took charge of two games when United scored four and didn't win. The first was a significant factor in his side's failure to win the 2012 title as United threw away a 4-2 lead and drew 4-4 with Everton at Old Trafford. The other was Ferguson's very last match, an extraordinary 5-5 draw at West Brom in 2013.

Amorim has a very long road ahead before he can be compared to Ferguson. But at least, on a night when his side led twice in the first half, then fought back to get their noses in front again after conceding two in a matter of minutes at the start of the second, and finally had to settle for a point as Bournemouth finished the stronger, he understood what everyone had witnessed.

In a vibrant first half, the hosts had the highest non-penalty xG value (2.49), most shots (17) and joint-most touches in the opposition's box (30) of any side in the opening 45 minutes of a Premier League match this season.

"If you understand a little bit," Amorim said. "If you follow the club like I follow the Premier League for so long, you [know you] have not just the duty to try to win the games. The way you try to win the games is so important for the fans.

"Of course they are desperate to win, but also, I feel that they are desperate to be inspired when they come to Old Trafford. Today was inspiring, I think, also because of Bournemouth. But in the end that's the feeling of frustration of not winning the game."

Former United captain Gary Neville agreed – kind of. "It might not be the greatest Man Utd team, and they might have problems at the back, but you can recognise it," he said. "It was a crazy game. The defences have been obliterated. It was absolute madness."

Neville was part of United sides who gambled to try to win rather than protect what they had. Ferguson regarded it as a key element of his managerial philosophy. The modern-day team are not at that level. And now, they have a problem.

This result means they have taken two points from three home league games most observers expected them to win. They have kept just one clean sheet in their 15 Premier League games this season, with only bottom side Wolves keeping fewer. They have also just had six shutouts in 42 games under Ruben Amorim.

Now they go to in-form Aston Villa not only without opening goalscorer Amad Diallo and dangerman Bryan Mbeumo, who join already absent Noussair Mazraoui on Africa Cup of Nations duty, but also missing veteran midfielder Casemiro, who serves a one-match ban after picking up his fifth yellow card of the season.

There was no hint at good news either over absent defensive pair Harry Maguire and Matthijs de Ligt. "We'll be ready for the challenge," Amorim assured United's legion of fans. "We already knew a lot of teams are going to lose players, a lot of teams have injuries.

"We just need to go for the next game with the responsibility to fight and win the game." Even during the game there was debate around how much Amorim tweaked his 3-4-2-1 system.

Former Republic of Ireland international defender Jim Beglin, covering the game for the Premier League's worldwide television feed, felt it was significant. Others felt it was slight, until Lisandro Martinez came on for Leny Yoro in the second-half and United definitely reverted to a flat back four.

The key was Amad, who was pushed further forward and instead of dropping into a wide defensive role in the first half hour, instead was inside Leny Yoro, who took the right-back slot. Iraola, whose own side reverted to five at the back after USA international Tyler Adams suffered a first-minute injury, felt it was "the same system they always play but they adapt. It is a very flexible system".

Amorim, who once said he wouldn't change the system even if the Pope asked him to, wasn't even getting into a debate. "That is for you to discuss, not me," he said. "I know that you guys know I trained this week with a back four but it is for you to discuss this week. "I will say the same thing, you can play with the same players and what looks like one thing is another."