A single goal by Alex Oxlade-Chamberlain was enough to give the Gunners victory with the Blues boss throwing his medal into the crowd before walking down the Wembley tunnel with Bobby Gill, aged 10, catching it.
The defeat is the first time Arsene Wenger has beaten the Portuguese and speaking after the game, Mourinho explained his actions.
"It's the medal for the loser... it's a good memory for him," Mourinho told BT Sport.
"Chelsea was the best team, had the more initiative, had good control, good ball possession.
But you know it is that moment of the season where everyone is behind - the energy, the intensity to turn results is more difficult because people is not sharp, and don't have intensity.
"Arsenal defended with a very low block, they defended with 10 men they put everybody in front of their line with very good organisation so... congratulations."
