Mr McGuinness, now the Northern Ireland Deputy First Minister, was asked to speak in the Cheshire town by Colin Parry, whose son Tim, 12, died in the blast.
Mr Parry said many people have criticised the decision to have him speak last night, but he believes it will send a message the peace process is a "very mature process".
He said: "I haven't forgiven the IRA for killing Tim, nor has anybody in my family and we never will," he said.
"But nonetheless we're pragmatic about the principles of building good relations across communities and across nations and I think you have to be quite hard-headed about it, and if I only ever did things on an emotional basis then I'd make some horrendously bad decisions.
"So this was a hard-headed decision to get Martin McGuinness to speak to a substantially Warrington audience, to explain his history perhaps, to talk about his present position on the arms struggle, and obviously I'll speak first, so I'll set the tone - it's an audacious event."
Tim Parry was fatally injured and Johnathan Ball, three, died instantly in the blast on March 20, 1993. Tim died five days later.