The Blues let a lead, given to them by Christian Pulisic, slip as Pierre-Emerick Aubameyang netted a brace for Arsenal.
His first came from a penalty after he had been fouled by Cesar Azpilicueta while Chelsea were hindered by injuries to the defender and Pulisic.
Mateo Kovacic was also sent off for two bookings though Lampard was not blaming the officials for their defeat at Wembley.
Speaking to the BBC, Lampard said: "We started well for 10-15 minutes and we can only blame ourselves from that point.
“We got complacent, we took time on the ball like it was a stroll and we allowed them into the game.
“It’s hard to get back into the game then. A lot of today is on us.
"All I can do from the sidelines is shout! There are elements in our game that we have worked hard on all year but that is in you as a group.
“Today we were slow, we played back on ourselves, invited pressure. We didn't play well enough to win a final.
"I'm not even thinking about next week, it all came together for us today, two hamstrings, a dislocated shoulder.
“It's the end of a long, long season and it was the tipping point for us."
It’s not been a bad debut season as Chelsea boss for Lampard with the Blues qualifying for the Champions League by finishing fourth in the Premier League.
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Lampard added: “There are some elements in our game we've worked hard on all year but some bits are in you as a group.
“We control games ... today we were slow, invited pressure. We didn't perform well enough to win the final.
“It all came together for us. We were below par, two hamstrings, dislocated shoulder [Pedro].
“Willian pulled up in training yesterday, [N’Golo] Kante wasn't fit. Ruben Loftus-Cheek out. It's not an excuse but it felt like a tipping point today.”