Watson said on Friday that Robinson appeared bitter and suffering a lot of stress and strain.
Robinson added another dramatic twist to the Essendon anti-doping saga on Wednesday night in a paid interview with Channel Seven.
He made a series of accusations, most particularly against Bombers coach James Hird.
Robinson added he had felt suicidal at times since he was stood down in early February.
He resigned last week and is considering legal action against the club.
"I felt as if there was a guy who was under a lot of stress and strain," Watson told radio station Fox FM.
"He looked like someone who had been very affected by what had gone on ... obviously he's not doing well and hasn't been dealing well with it.
"I think that my reaction was probably that there was his side of the story - it was very, I suppose, limited into a whole picture of what was happening at the club.
"I just thought that it was a little bitter in the way that he was conducting himself."
Watson said he could discount Robinson's allegations, but said the former Essendon employee had to back up what he said.
"There's one thing for you to say 'someone told me this happened' but to publicly come out and say it - you need factual evidence if you're going to make something like that public," Watson said.
Hird and Essendon chairman Paul Little have already denied several of Robinson's claims.
They insist Robinson is wrong in saying that police once raided Hird's home as part of a separate drugs investigation.
The two senior Essendon figures also said Hird had never asked Robinson to look into a so-called undetectable cream.
Little said Essendon was seeking legal advice over the interview.
The Australian Sports Anti-Doping Authority (ASADA) could be only days away from releasing the findings of its investigation into last year's controversial supplements program at Essendon.
The AFL is also investigating the issue.