Christ's anguish was expressed here in order to fulfill the prophecy of Isaiah. As Calvin explains in his commentary on Matthew 27:46...
"46. And about the ninth hour Jesus cried. Though in the cry which Christ uttered a power more than human was manifested, yet it was unquestionably drawn from him by intensity of sorrow. And certainly this was his chief conflict, and harder than all the other tortures, that in his anguish he was so far from being soothed by the assistance or favor of his Father, that he felt himself to be in some measure estranged from him. For not only did he offer his body as the price of our reconciliation with God, but. in his soul also he endured the punishments due to us; and thus he became, as Isaiah speaks, a man of sorrows, (53:3.) Those interpreters are widely mistaken who, laying aside this part of redemption, attended solely to the outward punishment of the flesh; for in order that Christ might satisfy for us, it was necessary that he should be placed as a guilty person at the judgment-seat of God. Now nothing is more dreadful than to feel that God, whose wrath is worse than all deaths, is the Judge. When this temptation was presented to Christ, as if, having God opposed to him, he were already devoted to destruction, he was seized with horror, which would have been sufficient to swallow up a hundred times all the men in the world; but by the amazing power of the Spirit he achieved the victory. Nor is it by hypocrisy, or by assuming a character, that he complains of having been forsaken by the Father. Some allege that he employed this language in compliance with the opinion of the people, but this is an absurd mode of evading the difficulty; for the inward sadness of his soul was so powerful and violent, that it forced him to break out into a cry. Nor did the redemption which he accomplished consist solely in what was exhibited to the eye, (as I stated a little ago,) but having undertaken to be our surety, he resolved actually to undergo in our room the judgment of God.
Your quote from Calvin contradicts the assertion you adduce it to prove.