The 27-year-old Croatian forward headed to Ukraine in a £6million deal during the summer after finding himself down the Gunners order following the free transfer signing of Marouane Chamakh.
Arsenal manager Arsene Wenger found it emotional to see the Brazil-born striker leave, after he fought back to full fitness following an horrific broken leg and dislocated ankle at Birmingham in February 2008.
Eduardo had vowed not to celebrate should he get on the scoresheet against his old club at the Emirates on Tuesday night - and was true to his word when netting a fine volley with seven minutes left after coming off the bench.
The Gunners fans, however, created a unique moment of sportsmanship in applauding the goal, which clearly touched the striker, whom Arsenal had signed from Dynamo Zagreb in July 2007 for a reported £7.5million.
"It was unbelievable", Eduardo told Arsenal TV Online.
"It was like I still play for Arsenal, when I came back and they started to call my name. It was fantastic.
"It was already 5-0, so that [not celebrating] was normal.
"But I was here for three years, had some great times with the manager, the players and the supporters, so I must respect this.
"I will continue to watch every Arsenal game on TV when I can.
"Now, though, I am a Shakhtar player and will give all best for them, like I did for Arsenal."
Shakhtar had also won both of their opening Group H games and came to the Emirates on an impressive run of form.
However, the Ukrainians were made to look ordinary by the Gunners, who barely got out of second gear after being set on their way following a terrible fumble by Shakhtar goalkeeper Andrei Pyatov which gifted Alex Song the opening goal on 19 minutes.
"We prepared well before the game, but on the pitch we did not do what we had to do," Eduardo said.
"But that is Arsenal - they are favourites to win against every team which comes here."