Noble had the chance to give the Hammers the lead in the first half at Upton Park after Kyle Naughton was penalised for handball, but he put his effort wide from 12 yards.
"I've always said to myself there will be a day when I do miss one. It's heart-aching to miss one against Spurs, but for sure I'll be stepping up for the next one we have," Noble told the club's official website.
"I knew where I was going with this one, I was going to whip it high in that corner, but I saw [Hugo] Lloris going and I just thought to go safe.
"It went wrong from there and it's obviously disappointing, but hopefully we don't get too down because it was a positive performance."
West Ham continue their Premier League campaign this Saturday when they travel to London rivals Crystal Palace.