Mr Molloy won the seat with 17,462 votes while his closest rival, agreed unionist candidate Nigel Lutton received 12,781.
The by-election was held after Mr McGuinness stepped down last year, as the party moved to end double-jobbing.
Speaking at the count centre in Cookstown on Thursday, Mr Molloy said: "[That may] take a wee while maybe but it's important to recognise that and I don't underestimate just what we are up against within that."
We were contesting against the deputy First Minister, so that was a very hard act to follow and hopefully we will fill those shoes.
The Assembly's outgoing principal deputy speaker, who will not take his seat in Westminster, had previously been accused of involvement in the murder of Mr Lutton's father.
The claims were made by DUP MP David Simpson in the House of Commons, under parliamentary privilege.
Mr Molloy has always denied the allegations, and said although overall it had been a fair fight, in recent weeks attempts had been made to "manipulate and cynically use" his past.
But Mr Molloy revealed he had greeted the Unionist candidate on Thursday, with Mr Lutton adding: "You've got to be decent to everyone."
There was a low turnout of 55% at the polls, which opened at 7am on Thursday and closed at 10pm the same day.
The Sinn Féin share of the vote reduced from 52% in 2010 to just under 47%, but Mr Molloy said that was to be expected in a by-election.
He was congratulated in his victory by the outgoing MP, Martin McGuinness, who held the Mid Ulster seat for 15 years.
The deputy First Minister blamed speculation about the election for the drop in votes for his party.
"The media said Francie Molloy is home in a boat, Nigel Lutton has no prospect whatsoever and I think a certain amount of complacency sets in," he said.
"For us it was a tremendous result of 17,000 votes. A great result for Francie Molloy and a great result for Sinn Féin."
But unionist voters made their voice heard as they cast their ballots and the DUP and UUP claim their share of the vote has increased.
"As a nobody coming in I was not expecting to increase the Unionist vote.
Mr Lutton said he was "relieved and humbled" to receive more than a 34% share.
The funeral director added that he had been described as "the undertaker that resurrected unionism."
Mr Lutton, a former member of the Victims' Forum, said the increased cooperation within unionism and raised vote "has made it all worthwhile".
However, he said following his three week campaign he had no major plans to continue a career in politics.
"One day at a time," he commented. "Back to work tomorrow."
Members of both the Ulster Unionist and Democratic Unionist parties supported Mr Lutton at the count centre, where UUP leader Mike Nesbitt congratulated their candidate and Sinn Féin.
"I hope that's the last time Sinn Féin fields an abstentionist candidate because that's yesterday's politics," he said. "I'm delighted for Nigel and for Mid Ulster. This changes Mid Ulster."
Two members of the UUP left the party when the plans to field a single unionist candidate were revealed, but that did not seem to faze Mr Nesbitt.
He described Mr Lutton's election quest as "an experiment" and said the results would be analysed, before hinting at further cooperation in future elections.
"I do not believe in unionist unity, this is unionist cooperation," he added.
SDLP MLA Patsy McGlone polled 6,478 votes, a rise of more than 3% since the 2010 election.
The Alliance party saw a rise of less than 1%, with their candidate Eric Bullick securing 487 votes.