The answer of your question is given by Shree-Krishna in Shreemad Bhagvat Maha Purana. ( Canto 11 ,Chapter 21 , Shlokas 29-30) SB 11.21: Lord Kṛṣṇa’s Explanation of the Vedic Path. Here
ते मे मतमविज्ञाय परोक्षं विषयात्मका:।
हिंसायां यदि राग: स्याद्
यज्ञ एव न चोदना॥29॥
हिंसाविहारा ह्यालब्धै: पशुभि: स्वसुखेच्छया
यजन्ते देवता यज्ञे: पितृभूतपतीन खला:॥30
te me matam avijñāya parokṣaṁ viṣayātmakāḥ hiṁsāyāṁ yadi rāgaḥ syād
yajña eva na codanā hiṁsā-vihārā hy ālabdhaiḥ paśubhiḥ sva-sukhecchayā
yajante devatā yajñaiḥ pitṛ-bhūta-patīn khalāḥ
Meaning - Those who are sworn to sense gratification cannot understand the confidential conclusion of Vedic knowledge as explained
by Me. Taking pleasure in violence, they cruelly slaughter innocent
animals in sacrifice for their own sense gratification and thus
worship demigods, forefathers and leaders among ghostly creatures.
Such passion for violence, however, is never encouraged within the
process of Vedic sacrifice.
Here is Swami Prabhupada's comentory on above shloka -:
The Vedic scriptures sanction occasional animal sacrifice to satisfy
cruel, low-class men who cannot live without the taste of flesh and
blood. Such concessions, however, are restricted by rigorous
obligatory rituals and are meant to gradually discourage animal
But unscrupulous persons misconstrue such restrictive sanctions and
declare that Vedic sacrifice is meant for killing animals in order to
enjoy sense gratification. Although understanding the authority of
Vedic rituals, they do not accept the ultimate Vedic conclusion and
therefore never surrender to God. Thus false religious principles
flourish in the demoniac societies of the animal killers.
So from above shlokas we can say that even though people are misinterpreting the meaning of allowance of Vedic-sacrific in limited manner , So in that sence ,Yes ,Vedas allow occasional sacrifice of innocent animal in Yagnas. however, is never encouraged within the process of Vedic sacrifice.
Note - As said in the above shloka we must first understand ,why it is allowed in vedas.( for the people who cannot live without the taste of flesh and blood).