Jose Mourinho might not have been too amused at Arsene Wenger's perceived handshake snub, but the Portuguese admitted Arsenal beat Chelsea at their own game in the Community Shield.

An Alex Oxlade-Chamberlain goal midway through the second half was the difference between the two London teams at Wembley, with Arsenal, once they went 1-0 up, showing great resilience in defence to quell the inevitable Chelsea pressure.

"For me it depends on the perspective. Normally you [the media] like to say a team that is defensive and defends very well doesn't deserve to win," Mourinho said.

"But I also have my opinion, different from your opinion. My opinion is the team that defends very well, that leaves their philosophy in the dressing room, changes their attitude, plays all the second half with nine players in front of the box, doesn't concede and scores one goal, from that perspective they deserve to win.

"This is football. This is very good tactical organisation. Congratulations to them."

That is more than Mourinho usually gives away in terms of a compliment after a loss, and much more so considering it is Arsenal. The 1-0 win for the Gunners also meant that 13-match winless streak coming to an end, with Wenger tasting victory for the first time against Mourinho.

The Chelsea manager again played down the relevance of the hold that he had over Wenger for so long at last coming to an end.

"I never had a psychological edge. It's not normal what happened before, and because it's not normal I never paid attention to that," Mourinho added.

"I always thought one game is one game and has no relation with other games. Thirteen matches is an eternity. It has never been a question of beating someone and losing to another one."

Chelsea played without Diego Costa in this Community Shield, and a lack of bite showed in the attack. Mourinho revealed the Brazil striker complained about a hamstring problem on Saturday, which forced the manager to start with Loic Remy, who failed to impress, much like the man who replaced him at halftime – Radamel Falcao.

"Two days ago he was ready to play," Mourinho said of Costa. "When I told you two days ago he was ready to play he was ready to play. He trained normally on Friday and yesterday at the end of the training session he said he was not feeling good.

"But Falcao will have had a bit more football, he will play against Fiorentina [in Chelsea's final preseason friendly on Wednesday] from the start. We have Remy too, so if we don't have Diego I am happy with the strikers I have."

Mourinho will, no doubt, use the International Champions Cup match against Fiorentina to get his team up to speed ahead of the Premier League opener on Saturday, with the Chelsea players, at times, struggling for that match sharpness, so essential in the big games.

"I expected the lack of sharpness, it's normal," said the Portuguese. "Some players like Falcao started a week ago. The others have had two weeks and half of this week. The pitch was a disaster, so slow, the weather didn't help too but it was the same for both teams so no excuses.

"I know Arsenal also like a good, fast pitch.

"One team played counter-attack football well. One team played with initiative well but without the sharpness you need to be more aggressive with the ball. The team tactically tried everything."