Satan can utilize the OT and NT. There is no scripture reference that says he only uses the OT.
Well now here are some verses about both. The Holy Spirit brings to remembrance(by quoting) the things that Jesus has ALREADY SAID TO YOU. Which when you read the new testament He is speaking to you.
John 14:26
26 "But the Helper, the Holy Spirit, whom the Father will send in My name, He will teach you all things, and bring to your remembrance all things that I said to you.
(NKJ)
John 16:13-14
13 "However, when He, the Spirit of truth, has come, He will guide you into all truth; for He will not speak on His own authority, but whatever He hears He will speak; and He will tell you things to come.
14 "He will glorify Me, for He will take of what is Mine and declare it to you.
(NKJ)
Satan doesnt do anything that glorifies Christ and Christ doesnt do anything that glorifies satan. They both have two different kingdoms. Satan has the old testament and Christ has the new testament.
Matt 12:25-28
25 But Jesus knew their thoughts, and said to them: "Every kingdom divided against itself is brought to desolation, and every city or house divided against itself will not stand.
26 "If Satan casts out Satan, he is divided against himself. How then will his kingdom stand?
27 "And if I cast out demons by Beelzebub, by whom do your sons cast them out? Therefore they shall be your judges.
28 "But if I cast out demons by the Spirit of God, surely the kingdom of God has come upon you.
(NKJ)