Bloomfield was sent off 14 minutes from time for the Chairboys but Ainsworth shied away from blasting the midfielder.
Ainsworth said: "We were the better team in the first half but we defended poorly in the second half.
"The conditions worsened in the second half and we took an onslaught from Bury and didn't handle it well.
"The sending off didn't help but it wasn't the reason we lost - there were other mistakes. I thought the goals probably were avoidable.
"We had a couple of chances early on in the second half to put the game to bed and you've got to take those because we got bitten on the backside late on and probably got what we deserved.
"We're better than that. We're young, and it's not an excuse but we're going to make mistakes and sometimes it looks very naive.
"I don't think we became complacent. I thought once we had a bit of an onslaught we panicked a little bit instead of keeping a calm head - and that's young kids for you."
Stewart gave Wycombe the lead from a corner, meeting Josh Scowen's cross at the far post to volley into the top corner.
But Soares grabbed a deserved equaliser for the visitors on 69 minutes when he finished Anton Forrester's clever cut-back.
Bloomfield was sent off for a rash challenge on Shaun Beeley before Edjenguele climbed highest to head home Chris Sedgwick's corner two minutes from time.