Rovers took the lead through Tommy Spurr's eighth-minute opener before Hanley's sending-off half an hour in for sticking an arm in the face of loanee Nick Powell.
Wigan substitute Grant Holt marked his first appearance since August by claiming an equaliser, although it may ultimately go down as a Spurr own goal.
Then fellow replacement Emmerson Boyce, who had captained Latics in their first ever home European tie just three days earlier, grabbed a stoppage-time winner.
But Bowyer had no idea why referee Stuart Attwell had instantly brandished Hanley's red card.
"I've not seen it again and I didn't see it in real time," said the Rovers boss, who also lamented the decision not to award a penalty when Jordan Rhodes' shot struck Ben Watson's arms.
"I didn't know what he got sent off for and as he came off I asked him what he did. I have to be honest I didn't understand him with the answer he gave me so I need to go and see it.
"It changed the course of the game because up until then we were very comfortable. We were pleased with how we were playing and we're disappointed to be leaving here without taking something from the game.
"Once the referee makes the decision there's an hour to play and our lads were magnificent."
Wigan boss Owen Coyle acknowledged his team were feeling the effects of a Europa League hangover but was more than happy to see the momentum shift once they gained a numerical advantage.
Coyle said: "They (Blackburn) have got something to hold on to taking the early goal but I felt we've grown into the game and then the lad's got the red card.
"He's been silly because he's been in control of the situation and he's thrown his arm out and there's no need to do it.
"I'm pretty sure Gary (Bowyer) will be upset by that."
- Sports & Recreation
- Tommy Spurr
- Emmerson Boyce