Lucescu was in charge of Inter Milan when they met the Red Devils in the Champions League quarter-finals just over 14 years ago.
Sir Alex Ferguson's side emerged triumphant, before recording victories against Juventus and Bayern Munich to lift the trophy for the first time under the Scot, who stood down after 26 years in the job last summer.
The transition is proving to be anything but straightforward.
United have lost three of their opening six Premier League games, their worst start since 1989, and travel to Ukraine with Ferguson's successor David Moyes under huge pressure.
"I played against Manchester United 14 years ago," said Lucescu.
"Then it was a machine for winning trophies.
"It was more of an English team then. Now it's more international, so it's quite difficult to compare these two teams."
A veteran of almost a decade's service at Shakhtar, 68-year-old Lucescu realises how much upheaval Ferguson's exit has caused at the Old Trafford outfit.
"Of course every coach needs some time to look at a new way," he said.
"There can always be some changes of philosophy and maybe that's why Manchester United are facing some difficulties in their championship.
"We have analysed their games and noted there are always some changes. Because of rotation the links between players are not very good.
"Turnover creates a lot of problems for them. In the Ukrainian championship we are not rotating the squad as much. Maybe that is why we have been more secure."
Not that Lucescu believes the current problems are any reflection on Moyes' ability.
"We know of Moyes' work at Everton," he said.
"He needs time to get his ideas across to the players. (Carlo) Ancelotti is having the same problem (at Real Madrid). (Jose) Mourinho (at Chelsea) and (Manuel) Pellegrini (at Manchester City) are the same.
"You need some time to prepare the team. Let's hope they find it but only after tomorrow's game."
Lucescu has every reason to be confident given Shakhtar's record at the Donbass Arena, venue for England's group games against France and Ukraine during Euro 2012.
When his side lost to Juventus in December last year it brought to an end an impressive 49-match unbeaten run on home soil.
Amongst their victims were Chelsea in a Champions League group Shakhtar cruised through from, whilst Arsenal have also been beaten twice in their impressive 52,000-capacity stadium.
And although they have subsequently lost two of their most high-profile players to the Premier League following Fernandinho's exit for Manchester City and Willian's departure for Chelsea, netting Shakhtar a combined sum of £60million, the club - who currently lie third in the table, having secured three successive domestic doubles - still boast an impressive squad.
Twenty-one-year-old Brazilian Bernard is a member of Luiz Felipe Scolari's present squad, full-back Darijo Srna is the current Croatia captain, whilst forward Alex Teixeira scored both goals in the away win against Real Sociedad on Matchday One a fortnight ago.
And, compared to Moyes, who will be taking charge of his first Champions League away game, Lucescu has 108 matches in the competition behind him.
Not that he feels it will make much difference tomorrow.
"Tomorrow is a Champions League game," he said.
"It's a whole different level of competition and we'll see a different Manchester United.
"Maybe it's more important not to lose points in the Champions League than the Premier League."