BOSTON — The state’s current and future political leaders moved quickly Wednesday to close – publicly at least – any lasting wounds from a bruising race for governor that ended with Republican Charlie Baker narrowly defeating Democrat Martha Coakley.

Baker spent about 45 minutes in a closed-door meeting at the Statehouse with Democratic Gov. Deval Patrick, who defeated Baker four years ago and had been sharply critical of the Republican on many occasions while stumping for Coakley. Baker, meanwhile, had highlighted management failings in the incumbent’s administration.

“Campaign’s over. We’re both looking ahead,” Patrick said standing next to Baker at a news conference after the meeting. “It’s really important to the commonwealth and the people that we serve and the people that the governor-elect will serve that his be a serious, thoughtful and helpful transition.”

Among the issues discussed during Wednesday’s meeting were the state’s ongoing transition to a new health insurance exchange and plans in case any Ebola patients emerge in Massachusetts, Patrick said.

Baker, who will take office in January, said earlier in the day that a “seamless” transition was his first priority, along with identifying talented people to serve in his administration.

“The voters responded to our message of focusing on the economy and focusing on educational excellence, and focusing on sort of that bipartisanship and balance on Beacon Hill,” said Baker.

Coakley, who waited until Wednesday morning to call Baker and formally concede the race, became emotional at times as she thanked supporters during a visit to her campaign headquarters in Somerville.

“Although Charlie is going to be our next governor, I feel like we both won,” Coakley said. “I feel we were both challenged and we both learned from this race, about ourselves and about Massachusetts.”

While Baker’s victory earns him a measure of political redemption, Coakley also had been looking for a comeback. She lost to Republican Scott Brown during the 2010 special election to fill the Senate seat left vacant by the death of Edward Kennedy.

The attorney general said she hoped Baker would address some of the themes of her campaign, including expanding early childhood education and reducing the stigma around mental health treatment.

“I told him I am going to hold him to his promises because I have his cellphone number now,” joked Coakley, who said she had no immediate plans for the future after completing her term as attorney general in January.

Baker named James Peyser, a former chairman of the state board of education, to head his transition team. Baker is former CEO of Harvard Pilgrim Health Care and was a top official under Republican Govs. William Weld and Paul Cellucci.

About 40,000 votes, or less than 2 percent, separated Baker and Coakley.

He raised more money than Coakley – an advantage that was magnified by the more than $8.6 million spent by outside groups supporting his candidacy, nearly all of it from the Republican Governors Association.

Asked Wednesday why the Democratic Governors Association did not provide the same level of support for Coakley, Patrick said simply that the DGA didn’t have the money.

Although the win by Baker and his running mate, Karyn Polito, was a breakthrough for the Massachusetts GOP, all other major races went to Democrats.

U.S. Sen. Edward Markey, who won a special election last year, easily defeated Republican Brian Herr to win a full term.

Seth Moulton, an Iraq war veteran who upset U.S. Rep. John Tierney in the Democratic primary, defeated Republican Richard Tisei in the 6th congressional district.

Two other incumbent Democratic congressmen who faced Republican challengers – William Keating in the 9th district and Niki Tsongas in the 3rd district – were re-elected. The state’s congressional delegation remained entirely Democratic.

Democrats also swept the other statewide races. Maura Healey was elected to succeed Coakley as attorney general and Deb Goldberg will take over asstate treasurer. William Galvin won a sixth term as secretary of state and Suzanne Bump a second term as auditor.

As for ballot questions, voters rejected measures that would have repealed the 2011 casino law and expanded the state’s bottle-deposit law but backed a question that would allow all workers to accrue sick time.

Voters also repealed a law that ties future increases in the state’s gasoline tax to inflation.