Daniel James Smith, 21, of Salford, admitted writing "Lee Rigby's killers should hang" on the memorial in central London on June 5, a monument he did not realise was a war memorial.
Colleen Gildernew, defending, said: "He had no idea that the war memorial was a war memorial. He is very disgusted with himself, even more so because of that."
Ms Gildernew told Westminster Magistrates' Court Smith had applied for a job in the British Army but was unsuccessful "because of his convictions as a young boy".
The court heard Smith has 44 convictions and has appeared in different courts five times this year.
Ms Gildernew said the experiences of Smith's two army friends - one who lost both legs and another who suffers from memory loss as the result of a bomb - had an "emotional impact on him".
The damage to the memorial, created to remember the thousands of RAF crew who died in the Second World War, amounted to £870.
District Judge Quentin Purdy described the content of the graffiti and its location, as "highly emotive". He remanded Smith in custody and adjourned sentencing until Tuesday.