Fans chanted Di Canio's name throughout the match as Swindon threw away a first-half lead given to them by Simon Ferry, with a late equaliser from Hartlepool's former Swindon winger Andy Monkhouse ensuring the spoils were shared.
Di Canio, who has felt let down by off-field events at the County Ground, said: "The supporters are magnificent and it has been a privilege to be manager of the club for the last year-and-a-half.
"But I stand by what I said before our match with Crawley that I am thinking about what happens next."
Town failed to make the most of the 15th-minute lead given them by Simon Ferry from close range after Gary Roberts had created the opening.
Goalkeeper Wes Foderingham prevented an equaliser with a good save from James Poole but it was Hartlepool counterpart, Scott Finders, who kept his team in the game.
Flinders made an outstanding double save Adam Rooney and Roberts in the 53rd minute as Hartlepool hung on desperately at times. But 12 minutes after coming on as a substitute for Poole, Monkhouse turned in a headed pass from Jonathan Franks after to earn Hartlepool a surprise point.
Di Canio said: "I am not happy. We dominated the game but we did not have top goalscorer to take the chances we created.
"We have been punished heavily because we were on top for so long and could have scored four or five. At the end of the season we might regret dropping these points.
"We do not have enough pedigree, mentality or nastiness and play less tippy-tappy. I am angry but these are best lads I have met in my life."