He also praised Bendtner, along with Moroccan forward Maroune Chamakh, for both getting on the scoresheet.
And Chamakh, 25, does not now envisage leaving Bordeaux before the transfer window closes on 1 September.
Bordeaux captain Alou Diarra hammered a volley against the bar before Marouane Chamakh bundled home from six yards.
"Without any hesitation, Arsenal was my preferred club, " said Chamakh, who hit 79 goals in eight years at Bordeaux.
Arsenal manager Arsene Wenger is not willing to meet Bordeaux's valuation of Chamakh, whose contract will expire next year.
Although born and raised in France, Chamakh qualifies for Morocco through his parents.
Marouane Chamakh slotted an early opener before Bendtner's superb header, then a curling finish, put Arsenal's second-string in command.
Boyata fouled Marouane Chamakh when he was the last defender five minutes in.
Lisandro Lopez put the hosts ahead after a mistake by Michael Ciani, but Marouane Chamakh headed in a 14th-minute equaliser.
Koscielny is Arsenal's second acquisition this summer, with Morocco striker Marouane Chamakh having joined from Bordeaux before the World Cup.
Arsenal chief executive Ivan Gazidis added that he was "delighted" the north Londoners had beaten off much competition to sign Chamakh.
Reina spilled the ball into his own net after Gunners striker Marouane Chamakh had bundled a Tomas Rosicky cross against the post.
BBC: Liverpool boss Roy Hodgson backs Pepe Reina after error
Chamakh's second goal was also the 1000th scored under Wenger's reign as Arsenal manager since taking over from Bruce Rioch in 1996.
Fabregas sent Chamakh racing clear and Boyata was the last man back as he clattered into the Moroccan striker just outside the box.
Wenger has recently admitted his interest in Bordeaux striker Marouane Chamakh, but the Morocco international is losing hope over any possible move to Arsenal.
The Gunners looked shell-shocked but eventually regrouped and, out of nowhere, Arshavin exchanged passes with Chamakh before drilling a magnificent first-time finish past Carson.
Chamakh claims he will commit himself to Bordeaux for the rest of the season if he has not found a new club by Monday.
It was not long before Arsenal were applying pressure and Nasri's free-kick was clawed away before Chamakh rattled the woodwork with a close-range header.
Captain Noureddine Naybet, Talal El Karkouri, Abdelsam Ouaddou and the France-based duo of Marouane Chamakh and Jawad Zairi are the notable absentees from the camp.
Chamakh was speaking ahead of his side's opening Ligue 1 match of the season in which he scored as Bordeaux beat Lens 4-1 at home.
"My bosses are trying to convince me to stay, " Chamakh said.
The lead lasted until the last minute when Marouane Chamakh diverted a cross against the post and Reina spilled the rebound into his own net.
The defender was sent off in the 64th minute for a clumsy challenge on Maroune Chamakh and after his absence Arsenal scored two further goals.
Bordeaux president Jean-Louis Triaud said on Wednesday that he would grant Chamakh his dream move to Arsenal if Gunners manager Arsene Wenger returned with a improved offer.
And with no Niklas Bendtner to call upon, Marouane Chamakh looks set to lead the striking line against Bolton at the Emirates with Andrei Arshavin offering support.
They have a lot of quality, including Arsenal's Marouane Chamakh.
"Chamakh is a striker of real quality and has all the attributes suited to come to England and do very well, " Gunners manager Arsene Wenger told the club's website.
Four minutes later, Chamakh's fourth Champions League goal of the season drew the visitors level, the Moroccan striker heading home after excellent work by Yoann Gourcuff on the right.
Chamakh's header from Bacary Sagna's cross was only inches away with Cech beaten, before Koscielny somehow headed the resulting corner over the top, despite standing almost on the goalline.
Arsenal were being punished for their wastefulness in front of goal, and Chamakh was the culprit again with 10 minutes left as he headed substitute Tomas Rosicky's cross wide.
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