Eduardo hopes he could be back in action for Arsenal when they kick off their FA Cup campaign at the start of January.
The Croatia striker played his first game after 10 months out with a broken leg in the reserves' 2-0 win over Portsmouth at Barnet on Tuesday but was brought off at half-time after feeling a twinge in his hamstring.
"I hope I can do more, and that next time will be better," Eduardo told Arsenal TV. "I just felt something in my hamstring, but in two weeks, I will be all right."
He added: "I need more training and games, and if everything is okay, then hopefully in two weeks I will be ready to play.
"I just want to play like I did before, but maybe I can be better.
"The injury was very hard for me, but I have had to forget everything bad in my life and went to do some treatment in Brazil where I saw my family and friends, which helped make me strong.
"The Arsenal fans and also in Croatia pushed me on. I have to thank all the medical staff as well."
The Gunners missed out on the chance to close the gap on the Barclays Premier League leaders when they could only draw 1-1 at Middlesbrough over a weekend when all the sides above them also dropped points, as they slipped down to fifth place behind Aston Villa.
However, Arsene Wenger's men have already beaten both direct rivals United and Chelsea, while current leaders Liverpool come to Emirates Stadium on Sunday.
"The team is improving, and if you look at the Middlesbrough game, we did have chances to score as well as being more stable defensively," said Wenger. "I am confident we will come back and catch some ground before Christmas and then push on."
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