Enner Valencia got a slight touch on Downing's corner with his hand before it bounced off Nedum Onuoha's knee and into his own net, but the officials allowed it to stand.
"I thought it was Enner who had scored, to be honest," Downing told Sky Sports. "I just tried to put it into an area and we had good lads attacking it.
"We were due a bit of luck and I think it's come off Onuoha in the end. It's gone against us in the past, but we've had the luck this time."
Senegal international Diafra Sakho headed in a second after half-time to make it five goals in as many starts for him personally, while West Ham also kept their first clean sheet of the season.
Downing, meanwhile, was the stand-out performer on the pitch, spreading passes around from a central position in midfield.
"I'm certainly enjoying it in there and we're playing some good football," he added. "With the good new signings we've had coming in, it's made the lads up there game even more with competition for places - and we all want to play."
There has even been some talk of the in-form 30-year-old getting the chance to add to his 34 international caps with England.
"I've said in the past that I'd love to play for England again, but I've got to be honest and realistic - I don't think that will happen at the minute," Downing commented. "If it does happen, I'd love to play, but we'll see what happens."
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