Ronnie Moore's Rovers were ruthlessly swept aside by a rampant attacking display from Town in which four goals were scored in a crazy opening 33 minutes.
Danny Hollands, Raffa de Vita, Andy Williams and Matt Ritchie put Town four-nil ahead at half-time, with Williams grabbing his second of the evening after the break before then missing the chance of a hat-trick when his penalty was well saved by Owain Fon Williams.
Di Canio said: "This was one of our best performances because we played against one of the best teams in the division, a solid team. I was sure we could win the match but not in this manner with so many goals. We created another six good chances.
"When you have the quality, the system, the detail and desire, as we did, this is what can happen. We have played similar games this season and not scored as many goals. This was a fantastic way to say thank you to the fans. But I warn everybody, we have done nothing yet and we have to keep going or we can burn what we have done."
Tranmere boss Moore was stunned by the result and pointed to a non-existent back four for his side's troubles.
"Shock is my reaction. We never saw this coming," Moore said. "The goals were from schoolboy errors and we did not exist as a defensive unit. But for our goalkeeper it could have been worse as we folded. Our back four was all over the place.
"We gift-wrapped four goals and then made a present of the fifth so we had not learned from our first-half mistakes. I could have ranted and raved but the team have been fantastic this season. I am hurting and I hope the players are hurting too.
"About 300 of our fans travelled down and they want to see better than that for their time and money.
"At half-time I could have taken off the entire team but you have to remember this is only our second away defeat of the season."