Arsene Wenger hailed Arsenal's "brilliant start" to the season following the 4-1 demolition of Portsmouth - but warned more challenges lay ahead.
Abou Diaby set the Gunners on their way with a first-half brace. Younes Kaboul pulled one back before the break - but a fluke from William Gallas and substitute Aaron Ramsey ensured a comfortable finish as Arsenal made it three wins from three.
"We have had a brilliant start," said Wenger, whose side meet Celtic on Wednesday before the next Barclays Premier League fixture at Manchester United. "It should create confidence and momentum. We now go into another week which will be another test against Celtic and then Manchester United. It looks to be exciting and interesting."
French midfielder Diaby marked his 100th game for the Gunners with an impressive display.
"When he decides to play more defensively, he is exactly like [Patrick] Vieira," said Wenger. "He has quick transition from box to box. When we are on the counter-attack, he is fantastic."
Arsenal captain Cesc Fabregas was replaced at half-time by Ramsey and Wenger revealed the Spain midfielder could be out for a fortnight if his hamstring problem proves serious.
Pompey boss Paul Hart was left to reflect on a "cruel" turn of events which cost his side a chance to get back to the match when, with the score at 2-1, last-man Gallas was adjudged not to have fouled John Utaka as the pair clashed on the edge of the penalty area.
"We got a foothold back in the game, and then there was an amazing decision when we are clean though to pop in an equaliser," said Hart. "I do not like to see people sent off, but that was a sending off offence. Gallas was the last man, and should have gone."
Hart maintains everyone at the club must stay positive, despite the continued off-field uncertainty.
"We can dwell on bad things, bemoan our luck, or you can dust yourself down and get on with it," said Hart, whose side have lost all three games. "There is no point moping around and feeling sorry. You can get on with it or walk away."
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