Wells scored the first goal as City produced another astonishing cup result - the League Two side beat Arsenal in the quarter-finals - and will head to Villa Park for the second leg in the box seat.
Bermudian Wells knows they may now be expected to finish the job and hopes they can do just that.
"We may well be the favourites now, but we want to be the underdogs," he told Sky Sports 1. "To get this far is great but we now want to make sure we get through.
"We showed our quality and that we can compete with Premier League teams. We were resilient, it was a tough match and we showed what we are capable of. To have a two-goal cushion is great.
"We would have taken a draw but 2-1, 3-1 is amazing. It's a good deficit to take with us to the away tie."
Rory McArdle made it two after Wells' opener, but Villa looked to have made a game of it when Andreas Weimann made it 2-1.
Carl McHugh had other ideas, though, with his late header putting Bradford into dreamland.
"It shows the team spirit we have," said goalkeeper Matt Duke.
"We've all put a shift in, credit to the boys in front of me, we caused them problems, scored three goals and we can go to Villa Park with a lead.
"We are playing a class team and we need to be on our game.
"It's a cliche but it's half a job and we have a bigger task ahead."