Liverpool Crown Court heard evidence from a victim who Bennell had admitted abusing in 1998, when he was jailed for nine years.
He told the court he tried to contact the parents of former Wales manager Speed, who hanged himself in 2011 aged 42, to tell them about the abuse.
The victim said: "Four people from teams I have played with, with Bennell, have taken their own lives."
He added: "Whether they have taken their lives due to Barry solely I don't know but all I know is how it's had an impact on me and how it could impact on other people."
He said he wanted to get in touch with Speed's parents because he had read in the paper that they had not been able to get closure because they had no explanation for his death.
Speaking about contacting other alleged victims of Bennell, the victim said: "When people are breaking down on the phone, on the verge of suicide, when you hear of people who have taken their own lives..."
Bennell denies 48 offences of child sexual abuse against 11 complainants between 1979 and 1990.
A flying winger in his youth, Gary Speed featured in the brilliant midfield quartet which underpinned Leeds United's Championship success of 1992, playing alongside David Batty, Gary McAllister and Whites captain Gordon Strachan.
Speed, a youth-team product at Elland Road, made more than 400 appearances for Leeds before joining Everton in 1996.
Speed was immortalised by a special moment of commentary from John Helm during a rousing win over Sheffield United in 1990. Speed inspired a 4-0 victory which kept Leeds on course for promotion from Division Two. “Go on Gary Speed, get one yourself son,” Helm urged as Speed broke away to score. Those words have proved timeless.