Let's begin with the basic LDS doctrine. From Moses 1:39:
For behold, this is my work and my glory—to bring to pass the
immortality and eternal life of man.
To us, immortality and eternal life are two things. The first is simply the continuation of the body through time. The second refers to the quality of our life in the hereafter. Building on this we find from LDS.org:
Eternal life is the phrase used in scripture to define the quality of
life that our Eternal Father lives. ... Immortality is to live forever as a resurrected
being. Through the Atonement of Jesus Christ, everyone will receive
this gift. Eternal life, or exaltation, is to live in God's presence
and to continue as families (see D&C 131:1–4). Like immortality, this
gift is made possible through the Atonement of Jesus Christ. However,
to inherit eternal life requires our "obedience to the laws and
ordinances of the Gospel" (Articles of Faith 1:3).
We therefore interpret Matthew 7:13-14 to refer to eternal life, not immortality, and indeed we believe few there will be who find it.
Now, to complicate the story a bit, the verb "to save" has a more complex meaning in LDS theology than it does in most other Christian religions. That's because we believe the "second death" referred to in Revelations 2:11 and 20:6,14 describes a permanent, spiritual death or separation from our Father and His Son. The Bible no longer describes the First Death (AofF 1:8), but the Book of Mormon does in 2 Nephi 9:15 (and other scriptures):
...when all men shall have passed from this first death unto life,
insomuch as they have become immortal, they must appear before the
judgment-seat of the Holy One of Israel....
For us, you can be saved from both the First Death and the Second. Everybody will be saved from the First Death (through resurrection), but only those who have availed themselves of the atonment of Jesus Christ to any degree will be saved from the Second Death. Doctrine & Covenants 76:43-44, which you quoted, clearly states that there are people who will receive no glory after judgement. These are they who died the Second Death. Everyone else receives some glory, depending on their faithfulness and willingness to obey the commandments of Christ and live according to His example throughout their lives.
However, the verse from D&C alone does not fully interpret Matthew. It draws the line between Perdition (which we more commonly name "Outer Darkness" and the other three kingdoms of glory (the Telestial, the Terrestrial, and the Celestial). Mathew is drawing the line below the Celestial, which we believe few will receive. The distinction doesn't bother us for a number of reasons begining with the fact that Jesus was giving instructions to two completely different sets of people for two completely different reasons. Anyone who has tried to give talks to different groups of people with known differences in their needs knows you can't write and deliver an entire book so that both deliveries provide all of the information both parties would need. So, why are we happy with the interpretation I've given you for Matthew?
It's because of Doctrine & Covenants 76:53-70(62), which teaches that our Heavenly Father dwells in the Celestial Kingdom, and Doctrine & Covenants 76:71-89(77, 86), which teaches people not in the Celestial Kingdom will be eternally separated from Him. Though not the Second Death because these people will enjoy some glory, they have not obtained eternal life, or life with our Heavenly Father.
We believe those exalted to the Celestial Kingdom will be few, and that this is what Jesus spoke of in Matthew.