London - Arsenal manager Unai Emery admitted his side must be self-critical of their performance despite edging up to third in the Premier League as David Luiz's first goal for the club earned a 1-0 win over Bournemouth on Sunday.
The Gunners had just two shots on target and were lucky to survive in the second-half as Callum Wilson spurned a huge chance to equalise for Bournemouth.
"We are very happy with that result. I'm very proud with our work in the first-half, but we are very critical with ourselves to improve things," said Emery.
"We spoke before the game that if we'd win, we would be third in the table and for our confidence it was important.
"Maybe in the second-half, we were winning 1-0, we were struggling more than we wanted and maybe in some moments we felt pressure."
It was at least an afternoon of relief for Luiz, who has been a figure of fun for a host of defensive errors early in his Arsenal career after making the switch across London from Chelsea in August
However, the Brazilian is always a threat at the other end of the field and rose highest to head home Nicolas Pepe's corner on nine minutes.
Pepe has struggled to match the expectations of his club-record 72 million ($88 million) transfer fee since a summer move from Lille, but was told by Emery to embrace the pressure of that price tag and the Ivorian was in the mood to impress.
Twice Arsenal had penalty appeals for fouls on Pepe by Diego Rico waived away.
However, it was Bournemouth who arguably had the best chance to add to the scoring before half-time when Dominic Solanke headed a Rico free-kick wide.
The visitors were certainly the more threatening side after the break and will rue heading back to the south coast with nothing to show for their efforts.
Wilson had the best chance when the England striker eased through the Arsenal defence and rounded Bernd Leno, but could not direct his shot on goal and Callum Chambers cleared.
Leno then had to be alert to turn Jack Stacey's driven shot behind.
Gabriel Martinelli was handed just his second Premier League appearance off the bench after the Brazilian scored twice in a stunning performance against Standard Liege in the Europa League on Thursday.
And he came close to a second Arsenal goal with a looping effort that drifted just over.
Emery's men then had to withstand a nervy five minutes of stoppage time as Matteo Guendouzi made a brilliant block to deny Josh King a certain equaliser and Steve Cook headed over from the resulting corner.
At the other end, Pierre-Emerick Aubameyang hit the woodwork in stoppage time as Arsenal nearly sealed the points in style, but one goal was enough for a vital win.