Teacher unions said that they were saddened when Mr Twigg lost the Enfield Southgate seat, as he had been an approachable and well-respected minister for school standards who had spent much time visiting schools.
David Hart, general secretary of the National Association of Headteachers, said: "The Government cannot afford to lose ministers of that calibre and I sincerely hope he gets back in as soon as possible".
Mr Twigg told The TES before the election that he feared that the Iraq war and a better-organised Conservative campaign might lead to him losing his seat by up to 2,000 votes.
His prediction proved accurate, as the Tories won back their former stronghold by 1,747.
This week he said he had been touched by the messages of condolence he had received from unions and schools and that he hopes to continue his work with teachers.
"After three years in the Department for Education and Skills there's a lot in my head about education and it would be a good thing to pursue," said Mr Twigg. "But whether that would be as an outside interest or a job I don't know yet."
He plans to take a few weeks to consider his options but Mr Twigg said that his experience in the election had not put him off politics. "Politics is in my blood," he said. However, standing again as an MP could be tricky.
"People say 'Oh, you will be offered a seat', but it will be a pretty complicated task to go back."