A brace from Chris Dagnall and a Marlon Harewood strike were enough to see off the Dons, who scored a consolation through Dean Bowditch and had Alan Smith sent off in injury time. There was also a serious injury to Barnsley midfielder Kelvin Etuhu and an altercation between Tykes' boss David Flitcroft and an MK Dons supporter.
Steele was a member of the Barnsley team who reached the semi-finals of the competition in 2008 and he is hopeful they can reach that stage once more. He said: "I love the FA Cup like every player I'm sure does and should."
He added: "It was a big match and the manager said before the game that we are fighting for a place in the quarter-finals of the FA Cup and when someone says it out loud it hits you that you've been in the situation before.
"Whoever we get it is not an issue, I was pleased with the last draw - coming here was still a massive challenge but the manager drilled it into us that we couldn't let off. We were so professional today, we got the job done in the end and we really deserve to be in the hat."
Etuhu was stretchered off the pitch during the second half after an accidental clash of heads with MK Dons' Adam Chicksen. Barnsley boss Flitcroft also confronted a fan who was aiming abuse at one of his players.
Flitcroft could not go into detail but said he was protecting his players and that a fellow MK Dons supporter had reported the abusive fan to the stewards, who promptly ejected him. Both MK Dons and Barnsley released a joint statement later in the evening to clarify matters.
"The spectator in question has been interviewed by Police; currently Thames Valley Police have no evidence to suggest the alleged gesture was of a racist nature," the statement read. "MK Dons will continue to monitor footage of the area where the alleged incident took place.
"Barnsley Football Club has placed on record its thanks to MK Dons FC, the stewards and the police for their professional and efficient handling of the situation.
"Both Barnsley Football Club and MK Dons Football Club are committed to making football a family-friendly environment and will not tolerate abusive or aggressive behaviour of any nature."