Morgan Rogers put Chelsea ahead inside the first minute before Kai Havertz levelled for Arsenal in the first half, and Martin Odegaard struck early in the second period to complete the turnaround. The result took Mikel Arteta's side to three wins from three, while Alonso's Chelsea suffered their first defeat since his appointment.
Alonso acknowledged the difficult spell after his early setback.
"It has been a game with different momentums, different stages. We started the game well, scoring first. The next 15 minutes, they were pushing us hard. We were defending low and struggled to get a little bit more, having the ball to be able to play a little bit more on the pitch," he said.
"So, yeah, those 15 minutes were hard and we had to suffer."
The Chelsea boss said his side showed character.
"We have had a couple of good chances before the end of the first half, but at half-time we spoke; it was a very close game, very intense, when we had to have a really high level of concentration, not to give many advantages to them, to be in the game, to be fighting for it," he said.
Asked if the defence, having conceded seven in three, was his priority, Alonso replied: "My priority is to win games and for that, normally it's easier when you don't concede many goals. So for sure, this is something that we need to address. We want to do better, we want to be tighter, to be more clinical, more balanced. But this takes time as well."
Arteta was delighted with the response after falling behind inside a minute.
"I think it was an exceptional performance. I think I enjoyed every minute of it from the beginning to the end, and the beginning was tough, but I enjoyed it because the team reacted in a spectacular way. The conviction, the determination, the quality of which I intend to have them constantly, it was beautiful," he said.
Arteta addressed the goal conceded.
"There are some things that we do badly in that goal that we discussed before, but credit to them as well, that from that ball in the air, somebody's able to put the ball very close to the post and score against David, which is not easy," he said, referring to goalkeeper David Raya.
Arteta was full of praise for Odegaard.
"Well first of all that he's fit, he feels confident, I think one of the highest that I've seen him, and he has a point to prove from last season as well, and after missing so much football," he said.