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It seems to me that looking for "feelings" at Mass is based on a misdirected intention. The Mass is not about how it makes you feel, primarily.
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Now, when you go to Mass with the proper intentions and the Mass itself helps you to recall what is important about your assisting at Mass, eventually (it might take some time, perhaps weeks or months) you will find that your feelings obey your efforts, your prayer and your intellectual actions. Our feelings are a thing in themselves, but they are a kind of thing that FOLLOWS your intellect. Feelings are a consequence of what you do and how you think, your outlook and attitude. 
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Perhaps the biggest principle missing in the Novus Ordo liturgy is the principle of SACRIFICE. If you go through the prayers of the liturgy and compare them to the TLM prayers, you will find that all reference to sacrifice has been removed. Traditionally, we talk about the SACRIFICE OF THE MASS, but there is rarely any mention of that term in regards to Novus Ordo services. But to make it more acceptable to Protestants, the 6 Protestant ministers who concocted the Novus Ordo texts deliberately edited out the word "sacrifice" and any mention of PENANCE or "works" since it was Luther's false teaching that there is no spiritual value in works.
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When the 3 Fatima children saw the angel with the flaming sword about to inflict the world with punishment (which Our Lady interrupted with her grace) the angel said, "PENANCE! - PENANCE! - PENANCE!" 
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In other words, the Message of Fatima is largely that we are not doing penance anymore, and we should.
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That was in the middle of "the Great War" (WWI) and war is a punishment from God.
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When you do hear "offering" or "gift" at Novus Ordo liturgies, it has been in my experience that it is heavily referenced to what is put in the collection basket or what items (bread and wine) that are paraded up the aisle to the altar. Usually it is someone from the congregation that carries these "gifts" to the priest. What we contribute for the support of our priests and the Church is important, but it is not EVERYTHING.
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Traditionally, we offer to God our gifts of self-denial, penitential works, voluntary acts of reparation, personal sacrifices, penance, moments of cheerful suffering that we have endured with the intention of giving to God our own personal gift of whatever we have endured for the reparation of sin - our own and the sin of others. St. Therese of Lisieux as a child made a string of beads with two cords going through both ways in each bead, and a bit of slack in the cords so the beads could be moved along the cords. When she met with a moment of challenge or discomfort in her daily life, she would offer it up, and move one bead along the cord. When she got to the end of the beads she would turn it around and do the same in the other direction, keeping track of how many times in the day she ran out of beads. When she went to Mass, she would recall that number and make it part of her Mass prayers as an offering to God. This is the foundation of her "Little Way" for which she became famous, mostly after her death, and is found in her book A Story of a Soul, which became a best seller.  It might be interesting to read the book looking for her thoughts on how she "felt" at Mass. As I recall, it is all centered on her feeling of how her voluntary acts of sacrifice were what she presented to God at the Offertory and the Consecration.
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When we have such things in mind when we pray the Mass with the priest, it makes us personally involved in the sufferings of Our Lord on the Cross, as we are able to "do what we can" to compassionate Him in His perfect act of redemption, which is the Mass.
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Anyone worried about "what I get out of Mass" should be focused on what we bring INTO the Mass. It is a matter of perspective, and intention. 
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The priest does not turn his back to the people, the priest is facing God, East and the tabernacle. Christian churches were always built with the altar facing East.

Women are feelings oriented, that is why the Novus Ordo is feelings oriented, it is run by and for women. The men who prefer the Novus Ordo are feelings oriented. ( prefer = are going to mass because they want to. They are not going to keep the wife happy, or because the children go to the Catholic school......). In the Novus Ordo in France, less than 4% of Catholics go to mass and they are all old ladies and the feelings oriented.