The Gunners chalked up a record 14 goals from their opening three Champions League Group H games, with Shakhtar going the same way as Braga and Partizan Belgrade as Arsene Wenger's side took control of Group H.
Another positive result for Arsenal, who will be without skipper Cesc Fabregas because of a hamstring problem, and the Premier League club could secure their place in the last 16 of Europe's elite once again.
However, since the thrashing in north London, Shakhtar have won all three of their domestic matches, without conceding a goal.
Arsenal have yet to record a victory in Ukraine, and with the Minors boasting an impressive record of only two defeats of their last 30 matches in all competitions, Lucescu believes his men can head into tomorrow's return fixture at Donbass Arena with some confidence.
"After analysing all the technical and tactical actions, I can say that the teams had about the same of the ball, 51% to 49%, and the passing also were about the same level," the Romanian said.
"We hope to show to our fans and the whole of Europe that now it will be a quite different Shakhtar.
"We have analysed the game that was in London to draw attention to the mistakes."
Lucescu added: "Not in any way do I think that Arsenal is stronger than Shakhtar. We will try tomorrow to demonstrate that on the field."
Arsenal never looked back after being gifted an early goal following a terrible fumble by Shakhtar keeper Andrei Pyatov.
However, Lucescu continues to lament a number of decisions by Swedish referee Svein Moen which he felt went in favour of the home side.
Swiss official Massimo Busacca, who took charge of the 2009 Champions League final between Manchester United and Barcelona, will be the man in the middle tomorrow night.
"I hope that tomorrow will be valid and neutral refereeing, which will help football in general. We will try to fulfil their responsibilities on the field," said Lucescu.
"The mistakes of the referee in favour of Arsenal were clearly visible.
"The third goal was not a penalty, the players pulled shirts together - and it should have been a red card for a hard [Jack] Wilshere reception against [Tomas] Hubschman.
"After three games, Arsenal has one card, while the rest of the teams have seven or eight. That says something.
"Therefore, we should double or triple our efforts to be at the level of this team or even higher."
Lucescu added: "I have been in European football for more than 25 years, so pay attention to what is happening.
"In recent years, some things happened, and I again had to take up the topic of judging comment.
"Scandinavian referees do not have the right to serve the games involving English clubs - that's my opinion.
"I make this conclusion not only on the game, which was in London. Throughout my career, such moments have taken place."
Former Arsenal striker Eduardo could face his old club again, having come off the bench to net a late consolation goal at Emirates Stadium, which received a round of applause from the home fans.
The Croatian, though, maintains there will be no thoughts of an 'old pals act' tomorrow.
"If we beat Arsenal we would practically be in the second stage, said Eduardo, who left in the summer after three years at Arsenal, having battled back from a broken leg.
"We are aiming to get at least to the quarter-finals of the Champions League - we can certainly do that, we've got a great team and all we need is a bit of luck."
Eduardo told UEFA Champions League Weekly: "Arsenal have always had difficulties against Eastern European teams and I am hoping they will find it the same this time.
"I know we are a good team and are always strong at home - the team have not lost a single match since moving to the new stadium."