Russia were just minutes away from their first win against the five-time world champions in their fifth meeting against them since the end of the Soviet era, but allowed Fred to score with a tap-in in the 90th minute to give Brazil a 1-1 draw in front of 35,000 fans at Stamford Bridge.
Although upset about the fan, who was quickly bundled away by stewards, Capello said he was happy with the result.
"I am happy with the way we played, we showed a lot of team spirit," the Italian told a packed media room.
"My only disappointment is that after a supporter came on the pitch my players lost their concentration and against Brazil you cannot lose your concentration."
Earlier another supporter had run on the pitch and was also quickly bundled away by security, but when Brazil coach Luiz Felipe Scolari was told what Capello had said, he replied with a story of his own.
"When I was a coach in Portugal we were playing against Estonia and a very beautiful girl came on the pitch topless, everyone was looking at her - even me. At the time the game was 0-0, and we ended up winning it 2-0.
"I don't know if the guy today distracted the Russian team, but who knows, it can happen."
Apart from the intruders, Capello said he was delighted with the way his team played as they chalked up their eighth unbeaten match.
"The most important thing I saw tonight was a great team spirit," he said.
"You need that as you build and go forward. It was a good result against Brazil and when when you play against a top team like Brazil you learn a lot about individuals and the team as a whole.
"I made some changes, brought some players in, and it takes us on another step towards our target. We can do something very important for Russia - which is to qualify for the World Cup finals in Brazil."
Russia, who will stage the 2018 finals after Brazil in 2014, took the lead with 17 minutes to play when Victor Faizulin found the net, but were undone in the dying seconds when Fred scored his third goal in the three matches Scolari has been back in charge of Brazil.
Capello, back in England where he coached the national team for four years, taking them to the World Cup in 2010, was asked what he thought of England's chances in their qualifier against Montenegro on Tuesday.
"It's not my problem," beamed the Italian, "and tomorrow I will probably watch the France v Spain game on the television."
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