Kourtney Hause grabbed a second-half winner, with Bruno Fernandes missing a 93rd minute penalty.
Solskjaer said: "You can take it when it's a good goal conceded against you, but that's offside. He's touched David as he heads the ball. How that's a goal and Leicester have not got their goals, I just can't see the consistency and that's clearly offside."
On the missed penalty, he continued: "I've not seen it because it ended up with nothing anyway so I can't comment on that one but unfortunately we missed the chance to get a point."
On the delay before the penalty and Villa players surrounding Fernandes, he added:"I wasn't going to mention it but it's not right that they do that. I guess that should be a yellow card for someone but they have achieved what they wanted.
"We were very aggressive, very good on transition, got forward quickly but the final shot, final pass and final decision wasn't always the best one. 20 of the 30 attempts were blocked."
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