BOSTON — Gov. Deval Patrick insisted Wednesday the state’s casino gambling law was “working exactly as it was supposed to,” and that he was not surprised by several recent votes against proposed gambling facilities.

The latest was in Milford, where Tuesday about 65 percent of voters who cast ballots in a binding referendum said no to a $1 billion resort casino plan offered by Foxwoods.

The vote came on the heels of rejections of proposed casinos earlier this month by voters in East Boston and Palmer, and in September by West Springfield voters. Those results leave the prospect that only a handful – if any – developers will be left to compete for the eastern and western regional resort casino licenses that the Massachusetts Gaming Commission could award next year.

Meanwhile, casino foes who have been gathering signatures around the state in the hopes of putting a question on the state ballot to repeal the 2011 law faced a 5 p.m. deadline to submit their petitions to city and town clerks.

Patrick told reporters that he’s had no second thoughts about signing the casino bill into law and did not want to see it repealed.

“I think it is working exactly as it was supposed to, which was to authorize up to three destination resort licenses and one (slots parlor) and to let people make their own decisions about whether they want the facilities in their own communities,” he said.

Patrick and other supporters of the law have said that the recent string of anti-casino votes is a validation of the law’s provision that requires local approval for any casino projects, and they have pointed out that several communities, including Everett, Springfield and Revere, have voted to welcome resort casinos.

Casino gambling can still succeed in Massachusetts, he said.

“I think this is something we can do well if we do it the right way. This has never been central to our economic growth strategy,” Patrick said after swearing in newly elected state Sen. Donald Humason, R-Westfield.

The group Repeal the Casino Deal needed the certified signatures of at least 68,911 registered voters to keep the proposed ballot question in play for the November 2014 state election.

David Guarino, a spokesman for the group, said it had already collected well above that number but was continuing to gather signatures up to the Wednesday 5 p.m. deadline, as a hedge against signatures that might be disqualified.

Guarino said the recent votes against casino projects have energized the repeal effort.

“We’re still David taking on the deep-pocketed casino industry Goliath but, after East Boston, Palmer and Milford just last night, Goliath is more than knocked down,” he said.