The Blues made a dream start to the London derby, taking the lead just 90 seconds into the game when Morgan Rogers found space outside the penalty area before unleashing a shot that put Chelsea ahead.
However, Arsenal gradually regained their footing and turned the match around, with Kai Havertz and Martin Odegaard finding the net to secure all three points for the Premier League champions.
The defeat left Alonso disappointed, with the Chelsea boss acknowledging that his team allowed Arsenal to dictate proceedings for long spells after taking the early lead.
Speaking to Sky Sports after the match, Alonso said Chelsea had opportunities to get back into the contest but ultimately failed to make the most of them.
“It has been a very intense game with different moments for everything.
“We had chances to equalise. In the first half as well a couple of chances. Never happy if you lose.
“After we scored, there were 15-20 minutes where we had to defend too much and we were struggling a bit to get control.
“We then had better spells with the ball. Overall, it was a very tight, very intense game. We could do better with the second goal to conceded too early. The guys gave everything, tried everything. It has to hurt.”
Chelsea’s defeat highlighted the fine margins in a game in which both sides enjoyed periods of dominance. Although the visitors responded positively after falling behind, Alonso’s men were unable to sustain their early advantage against an Arsenal side that grew stronger as the match progressed.
For Alonso, the result will be particularly frustrating given Chelsea’s bright opening and the opportunities they created to level the score.
The manager will now look for a response from his players in their next fixture as Chelsea seek to recover from the setback and maintain their push in the Premier League.