The statement “Crucifixion was not necessary for salvation and that only a drop of Jesus' blood needed to be spilled” could not have been from St. Thomas Aquinas. This is because it obliquely implies that there was no need for Christ to die, which is grossly against the tenets of Christianity.
St. Thomas was one of the supreme advocates of Eucharistic devotion and exponents of the nature of the mysterious process by which the host becomes the Body and Blood of Christ. Indeed, it was St. Thomas Aquinas who not only explained transubstantiation but also provided for the first time the word for it.
In his famous works “Summa theologiae” several times, St Aquinas stresses the importance of sacrifice of Jesus’ body and blood.
"The sacrifices of the Old Law contained only in figure that true sacrifice of Christ's Passion", whereas, "it was necessary that the sacrifice of the New Law instituted by Christ should have something more, namely, that it should contain Christ himself crucified, not merely in signification or figure, but also in very truth" (Summa, III, 75, 1, c.).
The Eucharist is, as it were, "the consummation of the spiritual life, and the end of all the sacraments" (Summa, III, 73, 3, c.).
The reason for this, St Thomas explains, lies in the fact that whereas the energy — "vis" or "virtus" — of the Passion of Christ is active in the other sacraments, the Eucharist contains "Christ's own Body" (Summa, III, 73, 1, 3m); ); in Scholastic language, Christ is present as "the common spiritual good of the whole Church... contained substantially in the sacrament itself of the Eucharist" (Summa, III, 65, 3, 1), in order to bring man to full communion with Christ in the Passion (cf. Summa, III, 73, 2, 3m).
St Thomas Aquinas also writes that
"in our pilgrimage, [Christ] does not deprive us of his bodily presence, but unites us with himself in this sacrament through the truth of his Body and Blood" (Summa, III, 75, 1, c.), always seen in their sacrificial condition".
Therefore, this statement is not in line with Catholic doctrine.
"And how much more does the Crucifixion do for us than a single drop of Christ's Precious Blood?"
While a single drop of Christ’s precious blood could cleans us from all sins, His death and resurrection was necessary for us to overcome the eternal damnation that came on us from our first parents. Our salvation is a result of death and resurrection of Jesus. The whole episode of crucifixion, including the circumstances leading to His crucifixion has been phrased as the passion of Christ and Jesus' physical torture including crucifixion was part of His punishment for our salvation.
The definitive plan of salvation began with the Fall of our first parents and the establishment of animal sacrifice as the one means of dealing with sin. Sin separated God's children from Him. There had to be a means to prevent eternal separation and that “means” became animal sacrifice by killing them and spilling their blood. Leviticus 17:11 explains God’s plan for forgiving sin.
God said to our first parents: For in the day that thou eatest thereof thou shalt surely die. (Genesis 2:17). If we were to take this “death” that God mentioned, as physical death then the same day they were supposed to have died. Here God was telling them about the eternal death not the physical death, which Adam died 930 years later (Genesis 5:5).
Physical death physically destroys the body but it is not an eternal destruction. The eternal death destroys the soul. Christ crucifixion, death and resurrection was necessary to overcome the power of this eternal death. With resurrection of Christ there will be a resurrection of all those who believed in Christ as He overcome the power of eternal death by His resurrection from death.
St. Thomas Aquinas:
Just as man was overcome and deceived by the devil, so also it should be a man who should overcome the devil. And since man deserved death so it should be a man who, by dying, vanquishes death. That is why it is written: 'Thanks be to God who has given us the victory through our Lord Jesus Christ [1 Cor. 15:57]. Summa Theologiae 3:46:4.
P.S. May be what Priest/layman said on Radio Relevant was: Death not necessarily by Crucifixion but by any other means. Or it may THIS issue.