Both the BBC and Sky News had refused to show the appeal made by the Disasters Emergency Committee (DEC) despite aid agencies saying hundreds of thousands of people were "in dire need" of food, blankets and water.
The appeal was shown by ITV, Channel 4 and Five.
As well as complaints made to the BBC, more than 170 MPs signed a motion criticising the stance taken by Sky and the corporation.
Trust chairman Sir Michael Lyons said he and his colleagues recognised that Mr Thompson's decision was "a matter of great controversy for many members of the public".
Sir Michael Lyons: 'Our job is not to second guess the Editor in chief'
But the Trust had concluded that decision was "reasonable given the importance of preserving the reputation of the BBC for impartiality".
Sir Michael said: "The director general argued that the Israeli-Palestinian conflict is deeply divisive and that the suffering of civilians plays a central part in the political case each side makes in the 'court of world opinion'."
Mr Thompson had consequently thought it "impossible in this case to separate the political causes from the humanitarian consequences", Sir Michael added.
In the director general's view, the appeal would, by its very nature, have shown only one aspect of the conflict
Sir Michael Lyons
"In the director general's view, the appeal would, by its very nature, have shown only one aspect of the conflict and broadcasting it, he argues would have implied a significant level of the endorsement by the BBC of the appeal itself - thereby putting BBC impartiality at risk."
Sir Michael said the Trust had found this to be "a reasonable argument" and that the decision taken was "within the parameters of reasonable decisions open to him".
Judicial review threat
The Trust said the BBC and other broadcasters should look again at their agreement with the DEC on when appeals should be screened.
It was drawn up in 1971 before the days of 24 hour news channels and the internet, and before the existence of channels like Sky News which broadcast both in the UK and internationally and so have to satisfy different audiences' expectations of impartiality.
The DEC responded to that suggestion with a written statement,
"We respect the BBC's right to decide on whether to broadcast the appeal but we believe it would be unfortunate if the additional hurdle imposed in this specific situation set a precedent for future appeals.
"The three criteria agreed with broadcasters for launching DEC appeals - scale of need, ability of DEC members to deliver aid, and evidence of public support - have stood the test of time."
The BBC's management rejected complaints from members of the public about the decision not to screen the appeal but a number of complainants appealed to the Trust.
They included two residents of Gaza and one person living in the UK who lodged a detailed appeal through law firm Hickman and Rose.
The firm said it was now highly likely it would be applying for judicial review of the decision.
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