Churches associated with Reformed theology actually have a variety of views on the gifts of the spirit – many are in the "continuationist" camp. But among those that are cessationist, their views long precede Pentecostalism.
The Westminster Confession of Faith, 1.1, like most varieties of cessationists, rejects the possibility of new Scripture:
Therefore it pleased the Lord, at sundry times, and in divers manners, to reveal himself, and to declare that his will unto his church; and afterwards, for the better preserving and propagating of the truth, and for the more sure establishment and comfort of the church against the corruption of the flesh, and the malice of Satan and of the world, to commit the same wholly unto writing: which maketh the Holy Scripture to be most necessary; those former ways of God's revealing his will unto his people being now ceased.
Jonathan Edwards (1703–1758) was a strict cessationist:
It is this miraculous gift [prophecy] which the apostle here says shall vanish away, together with the other miraculous gifts of which he speaks, such as prophecy, and the gift of tongues, &c. All these were extraordinary gifts, bestowed for a season for the introduction and establishment of Christianity in the world, and when this their end was gained, they were all to fail and cease. (Charity and its Fruits, 439)
Other cessationists generally hold this but aren't quite so adamant. For example, John Calvin:
Those who preside over the government of the Church, according to the institution of Christ, are named by Paul, first, Apostles; secondly, Prophets; thirdly, Evangelists; fourthly, Pastors; and, lastly, Teachers (Eph. 4:11). Of these, only the two last have an ordinary office in the Church. The Lord raised up the other three at the beginning of his kingdom, and still occasionally raises them up when the necessity of the times requires. (Institutes, 4.3)
All these writings long precede Pentecostalism, and all these views are shared by many Reformed cessationists today. Thus it wouldn't be fair to say that Reformed cessationism is a reaction to Pentecostalism, though for some individual Reformed thinkers that may be the case.
And as mentioned before, there is such a thing as a Reformed continuationist. Wayne Grudem is a prominent example, but even at the time of the Reformation some fit that category, such as John Knox.
So it's important to note that at the time of the Reformation, just like today, there are Reformed theologians who are cessationist and others who are continuationist. The biblical arguments they use to defend their views haven't changed much either – overall, the rise of Pentecostalism has not directly influenced Reformed cessationism.