The only goal on an uninspiring night, when Wembley was wrapped in autumnal gloom and travel problems meant there were thousands of empty seats at kickoff, came after 35 minutes through Ashley Young.
England, though, are now within a point of qualifying for next year's finals in Poland and Ukraine.
Wales had a gilt-edged chance to equalise after 76 minutes when the ball fell to substitute Robert Earnshaw five metres out and the striker blasted the ball high over an open goal.
"Yes I think we were a bit lucky, they made a big mistake in front of goal [through Earnshaw] but that was our luck," a relieved Capello told reporters.
"In the last 15 minutes we suffered a bit and didn't play good passes. We never pressed the ball, we were without speed... we survived the last 15 minutes."
The Italian lamented another poor England performance in front of 77,000 fans who braved a torrential storm and problems on the Underground and nearby roads.
It was England's first win at home in five matches since they beat Bulgaria a year ago but they struggled for long periods.
"We seem to lose confidence at Wembley," said Capello. "Some players that usually dribble and go straight at goal don't do it here.
"We pass across the goal four or five times. I want always three players in front of the goal, tonight there was one.
MORE COURAGE
"When we play at Wembley we want to play with more courage," Capello added. "Before we qualified for the 2010 World Cup we played very well here but when there is pressure to get the result it's hard."
Wales manager Gary Speed was pleased with his side's second-half showing.
"We were unlucky. I think we played a great second half," said Speed. "We knew coming to a place like this and playing the fourth-ranked team in the world we were going to come under pressure.
"We created a few chances and were unlucky not to score with the Earnshaw chance. There was also a chance where Gareth Bale was one-on-one with the keeper and he was ruled offside when he was actually one-metre onside.
"That didn't go for us today but I'm really proud of the players. How comfortable they were on the ball in the second half against a top team was really good," said Speed.
The Wales coach said he drew plenty of positives from the performance of his team.
"There's not an awful lot we could have done about the goal and we limited England to very few chances," added Speed.
"Once the game opened up I thought the way we passed the ball was exceptional. We'll take a lot of positivity from this for the future.
"But we've had false dawns in Wales before and we can't afford another false dawn. We've got a lot of hard work to do if we want to keep progressing," said Speed.
