Text of original answer
Catholic doctrine holds there are two participations in the one priesthood of Christ: the ministerial or hierarchical priesthood of bishops and priests (presbyters), and the common priesthood of all the faithful (CCC 1546-1547) . In this regard, deacons side with all the faithful, not with bishops and priests.
Thus, while the sacrament of Holy Orders confers three degrees of ecclesiastical ministry: bishops, priests, and deacons, "there are [only] two degrees of ministerial participation in the priesthood of Christ: the episcopacy and the presbyterate. The diaconate is intended to help and serve them. For this reason the term sacerdos in current usage denotes bishops and priests but not deacons." (CCC 1554) .
 The Sacrament of Holy Orders in the Economy of Salvation (Vatican Website)
 The Three Degrees of the Sacrament of Holy Orders (Vatican Website)
Additional text in response to comments
While my original answer pressuposed the (presumably well-known) notion that "Catholic doctrine also holds that the Eucharist can be celebrated and the sacraments of Confirmation, Confession and Anointing can be administered only by men who have received the ministerial priesthood, while the sacrament of Holy Orders can be administered only by bishops.", commenters asked for the basis of that notion. I assume it is also well-known that Catholic (as well as Eastern Orthodox) doctrine is not based exclusively on Scripture but also on Apostolic Tradition, which is witnessed by the writings of the Church Fathers. One page which offers a list of such writings on this subject is . Having said this, I will only touch briefly the biblical support of ministerial priesthood as distinct from the common priesthood of all the faithful.
1. That there is a ministerial office held only by the apostles and those appointed by them is clear from what Paul tells the Corinthians regarding himself, Apollos and Cephas (Peter):
"Let a man regard us in this manner, as servants of Christ and
stewards of the mysteries of God." (1 Cor 4:1).
Otherwise all the faithful would be "servants of Christ and stewards of the mysteries of God", not just Paul, Apollos and Cephas.
2. The way in which this ministry is passed on to others is stated in Paul's letters to Timothy:
"Do not neglect the spiritual gift within you, which was bestowed on
you through prophetic utterance with the laying on of the hands of the
presbytery." (1 Tim 4:1)
"For this reason I remind you to kindle afresh the gift of God which
is in you through the laying on of my hands." (2 Tim 1:6)
That Paul included himself in the presbytery in the first passage is consistent with this passage from Peter:
"Therefore, I exhort the presbyters among you, as your fellow
presbyter and witness of the sufferings of Christ, and a partaker also
of the glory that is to be revealed," (1 Peter 5:1)
This is consistent with Catholic doctrine because, in current terminology, all bishops are presbyters, though not all presbyters are bishops.
That Timothy should, in turn, pass on the ministry to others is implicit in:
"Do not lay hands upon anyone too hastily and thereby share
responsibility for the sins of others; keep yourself pure."
(1 Tim 5:22)
3. For three sacraments, the NT states clearly that they can be administered only by the apostles and those who have received their ministry from them.
3.a. Holy Orders. Clearly stated in the above quotes from Paul to Timothy.
The book of Acts states clearly that the gift of the Holy Spirit (current sacrament of Confirmation) was given through the laying on of an apostle's hands, not of a deacon's hands:
"Philip [the deacon] went down to the city of Samaria and began
proclaiming Christ to them. [...] But when they believed Philip
preaching the good news about the kingdom of God and the name of Jesus
Christ, they were being baptized, men and women alike. [...] Now when
the apostles in Jerusalem heard that Samaria had received the word of
God, they sent them Peter and John, who came down and prayed for them
that they might receive the Holy Spirit. For He had not yet fallen
upon any of them; they had simply been baptized in the name of the
Lord Jesus. Then they began laying their hands on them, and they were
receiving the Holy Spirit." (Acts 8:5,12,14-17)
3.c. Anointing of the sick
Clearly stated in James's letter:
"Is anyone among you sick? Let him call near the presbyters of the
church, and let them pray over him, having anointed him with oil in
the name of the Lord. And the prayer of faith will save the one
ailing, and the Lord will raise him up, and if he might be one having
committed sins, it will be forgiven him." (James 5:14-15)
4. Eucharist and Confession.
So far, it is clear from the Bible that there is in the Church a ministry received by the Apostles, and passed on by them to presbyters but not to deacons, which enables those who receive it to impose the hands to give the Holy Spirit, to anoint the sick, and to transmit the ministry itself through the laying on of the hands (the latter restricted to bishops, who are a subset of presbyters). Now, does that ministry include the exclusive capacity to celebrate the Eucharist and to forgive sins? In other words, do Jesus' words to the Apostles
"do this in remembrance of Me." (Lk 22:19; 1 Cor 11:24)
"If you forgive anyone's sins, they are forgiven; if you retain
anyone's sins, they are retained." (Jn 20:23)
apply only to the Apostles and those who are passed on their ministry from them, or to all the faithful?
The answer to this question is not found in the NT but in the Apostolic Tradition.