The Russians thoroughly dominated the visitors but failed to hit the target until Shirokov calmly converted the 84th-minute spot-kick following a foul on substitute Vladimir Bystrov.
Video replays showed the foul was committed outside the box but Azerbaijan coach Berti Vogts said the home team deserved to win.
"I can only congratulate Russia on their victory," former Germany boss Vogts, who has been coaching the oil-rich country on the Caspian Sea since 2008, told reporters.
"We fought hard but overall they played better than us. As for the penalty kick, I didn't see the replay yet. Nevertheless, there's no point in discussing the referee's decision now."
"Of course, it would have been much easier for us if we scored an early goal," said Italian Capello, who replaced Dick Advocaat as coach following Russia's poor showing at Euro 2012.
"But you have two teams on the pitch. Azerbaijan have become a very organised team under Berti Vogts, so today we had a very tough opponent."
The visitors, missing injured captain Rashad Sadygov, rarely troubled Russia keeper Igor Akinfeev, who set his country's all-time record, including Soviet times, by keeping a clean sheet for the eighth consecutive game.
"[Akinfeev] is one of our best players. He is largely responsible for us winning these four qualifiers without conceding a single goal," said Capello.
Russia stayed top of the group on 12 points from four games and Azerbaijan have one point following a 1-1 draw against Israel in last month's opener.
