Most sacrifices were completed by sprinkling some blood from the sacrifice on the altar. And in one specific case (Lev 16) on the mercy seat (or atonement cover). Since Jesus’ death was a sacrifice, it might make sense that his blood should be sprinkled on the altar. But there’s no evidence that this happened, nor any obvious way for it to happen (not that Jesus’ blood hasn’t aroused much notoriety over the years).
Instead, when Jesus died, the curtain in the temple was torn. The symbolism of this was clear, and Hebrews says:
Therefore, brothers, since we have confidence to enter the Most Holy Place by the blood of Jesus, by a new and living way opened for us through the curtain, that is, his body, and since we have a great priest over the house of God, let us draw near to God with a sincere heart in full assurance of faith, having our hearts sprinkled to cleanse us from a guilty conscience and having our bodies washed with pure water. (Hebrews 10:19-22 NIV)
So it seems that it wasn’t necessary for Jesus’ literal blood to be sprinkled on the altar — after all, the whole sacrifice business was just a symbol pointing forwards to Jesus.