Deeply connected to devotion to the Sacred Heart is a greater love of Jesus' presence in the Holy Eucharist.
St. John Paul II explained this connected in a letter he wrote on the 100th Anniversary of the Consecration of the World to the Sacred Heart:
The entire devotion to the Heart of Jesus in its every manifestation is profoundly Eucharistic: it is expressed in religious practices which stir the faithful to live in harmony with Christ, "meek and humble of heart" (Mt 11:29), and it is intensified in adoration.
Source and summit
He further explains how the Sacred Heart devotion is intimately connected to the celebration of Mass:
It is rooted and finds its summit in participation in Holy Mass, especially Sunday Mass, where the hearts of the faithful, fraternally assembled in joy, listen to the word of God and learn to offer with Christ themselves and the whole of their lives (Sacrosanctum Concilium, n. 48). There they are nourished at the paschal banquet of the Redeemer's Body and Blood and, sharing fully the love which beats in his Heart, they strive to be ever more effective evangelizers and witnesses of solidarity and hope.
St. John Paul II also added how, "Contemplation of the Heart of Jesus in the Eucharist will spur the faithful to seek in that Heart the inexhaustible mystery of the priesthood of Christ and of the Church."
Pope Benedict XVI also commented on this link in his 2011 homily on the feast of Corpus Christi:
[T]he Eucharist is the food of eternal life, the Bread of Life. From Christ’s heart, from his “Eucharistic prayer” on the eve of his passion flows that dynamism which transforms reality in its cosmic, human and historical dimensions. All things proceed from God, from the omnipotence of his Triune Love, incarnate in Jesus. Christ’s heart is steeped in this Love; therefore he can thank and praise God even in the face of betrayal and violence, and in this way changes things, people and the world.
Both devotions complement each other and should ultimately lead to a deeper love of God.