Gotcha. We don't teach grace is imparted solely from the Eucharist. We wish all people could eat and drink worthily. If you cannot we ask that you refrain. It's that simple. It is desirable, it SHOULD be the most desirable thing in the world. But your state of grace determines whether you can eat and drink it worthily, not the other way around.
I assume you mean that the Eucharist is not the as the "only" method of imparting grace. That is true. If memory serves me correctly there are seven sacraments, the Eucharist being one of them. But the Church teaches that grace is imparted through the Eucharist (as one method).
And forasmuch as, in this divine sacrifice which is celebrated in the mass, that same Christ is contained and immolated in an unbloody manner, who once offered Himself in a bloody manner on the altar of the cross; the holy Synod teaches, that this sacrifice is truly propritiatory and that by means thereof this is effected, that we obtain mercy, and find grace in seasonable aid, if we draw nigh unto God, contrite and penitent, with a sincere heart and upright faith, with fear and reverence. For the Lord, appeased by the oblation thereof, and granting the [Page 155] grace and gift of penitence, forgives even heinous crimes and sins. - Council of Trent, 23rd Session