The Barclays Premier League champions were sluggish as their London rivals, through Alex Oxlade-Chamberlain's 24th-minute goal, recorded a rare victory against them.
The winger's powerful finish was Arsenal's first goal against Chelsea in 506 minutes, and ended the Blues' eight-match unbeaten run against them.
Terry remained adamant that they were the superior side and refused to dismiss the fixture as a friendly and hoped the defeat would ensure that they were better prepared.
"There was a trophy on the line," said the 34-year-old, whose side host Swansea on Saturday in their opening Premier League fixture
"It hurt when you saw them walk up the [Wembley] stairs to lift it
It means a lot because you work all season to be here
They earned the right to be here by winning the FA Cup
So did we by winning the league
"No matter if it's a friendly or a Community Shield - it's a trophy at the end of the day
It's horrible
It's not nice
At the same time, it could be a blessing in disguise for us - a wake-up call.
"We have experience in the squad - we have the character
It's going to be even tougher this year
We go again and prepare ourselves for Swansea.
"We have the Premier League to concentrate on now
We have to take the positives from it
We got another 90 minutes under our belts."
Chelsea had only returned from a pre-season largely spent in the United States on Wednesday while Arsenal, who resumed training a week earlier than Jose Mourinho's team, appeared fresher.
Terry and his team-mates also struggled against fatigue towards the end of last term - their impressive start was ultimately what inspired them to the title - but the defender insisted their conditioning was not a concern.
"I don't think so," he replied when asked if Chelsea were tired
"I thought we were on top, if anything
I think these games are always a bit slow anyway - the players are still finding their feet and fitness.
"[Losing's] horrible, whether it's against my kids or anyone
That's the mentality I was brought up in
That's the same as the manager on a daily basis.
"It was a different atmosphere in the dressing room afterwards
We haven't lost many at Wembley
It's maybe the boost we needed and we go again for the season."
The defeat means Chelsea's pre-season is at risk of concluding without a solitary win in normal time.
Gary Cahill resumed his central defensive partnership with Terry, but was unconcerned about their form and instead maintained that they should be judged from Saturday, when the league season begins.
"Pre-season is false in many ways because you're changing the team, everyone's getting minutes, everyone is trying to get fit and you're training hard," he said.
"You're doing double training sessions before you play a game
We still have another week of that before we get down to business against Swansea.
"I thought the game was opened up by a bit of individual brilliance - [Oxlade-Chamberlain] came inside and hit it into the top corner
Apart from that, I don't think they had too many chances."
Source : PA
Source: PA