The Hoops boss had yet to see footage of Marc-Antoine Fortune's disallowed goal and Kyle Lafferty's horror tackle on Andreas Hinkel.
Having now had time to watch both back, Mowbray insists Lafferty should have been sent off and Fortune's header allowed to stand.
He said of Lafferty's studs-first challenge on Hinkel: "I cringed at the time, and when I saw it back, my reaction was still the same.
"I talked last week about protecting players like Aiden McGeady, but my point was really about officials having total concentration on the game.
"Officials have to get big decisions right - especially when they are potentially game-changing decisions.
"I am the last person who wants players sent off but, again, when the referee looks at that re-run, he will think he didn't get it quite right.
"Generally, the referee did okay and kept the game going, but when you look back at those two incidents in isolation, it does seem that we were a bit hard done by."
Fortune saw a goal chalked off when the game was goalless after he beat Rangers goalkeeper Allan McGregor to the ball to head home.
Mowbray told Celtic View: "Watching the replay of the incident with Fortune in cold reflection, I find it difficult to see a free-kick.
"In those situations, I always try to put myself in the mind of the referee.
"I say to myself, 'Can he see a foul there?'
"And does he sit at home afterwards and think, 'That's why I blew my whistle'.
"Personally, I still find it very hard to see a foul.
"What can we do though? It's been discussed and will be discussed.
"But, as the Irish found out after Thierry Henry's handball in the World Cup qualifier, the result doesn't change and you don't get another chance to play the game.
"But it's disappointing because I don't see any infringement when the ball gets headed into the net."
Sunday's result left Celtic seven points behind Rangers with a game in hand.
The home side, who today saw Saturday's Active Nation Scottish Cup tie at Morton postponed due to the big freeze, dominated the game and Mowbray believes his side have proven they have the measure of their arch-rivals this season.
"We should have nothing to fear in the future derbies after the way we've played in the first two games," he said.
"What we need to do is convert our pressure and chances into goals."