Prosecutors presented photos of three panels of the boat that had messages written in pencil.
Boston police Officer Todd Brown, a bomb squad member who cleared the boat of explosives, was on the witness stand to talk about the writings.
Tsarnaev is charged with 30 counts related to the April 15, 2013, bombings that killed three people and wounded more than 260 others.
A fourth person, an MIT police officer, was ambushed and killed in his patrol car three days after the bombings as Tsarnaev and his brother, Tamerlan, allegedly ran from police.
Tamerlan Tsarnaev, 26, was killed after a gunbattle with police.
On Tuesday, Brown identified Dzhokhar Tsarnaev in court as the man he saw come out of the boat and get taken into custody.
In the writings on the panels, some of Tsarnaev's words were struck out by bullet holes.
"I'm jealous of my brother who ha (bullet hole) ceived the reward of jannutul Firdaus (inshallah) before me," one of the writings said, referring to the word for paradise. "I do not mourn because his soul is very much alive. God has a plan for each person. Mine was to hide in this boat and shed some light on our actions."
Tsarnaev's defense has argued that he indeed participated in the bombings, but that he was influenced by his radicalized brother.
In his writings on the boat, Tsarnaev asked Allah to allow him to reach the highest levels of heaven.
"The US Government is killing our innocent civilians but most of you already know that. As a (bullet hole) I can't stand to see such evil go unpunished. We Muslims are one body, you hurt one you hurt us all. Well at least that's how muhhammad (bullet hole) wanted it to be (for)ever," Tsarnaev wrote in the boat.
Also Tuesday, prosecutors called on FBI agent Steve Kimball to discuss two Twitter accounts linked to Tsarnaev.
One, @J_tsar, contained 1,100 tweets and was the more mainstream of the two.
"I shall die young," @J_tsar tweeted on April 12, 2012.
And four days later, on the day of the 2012 Boston Marathon, a tweet from the account read, "They will spend their money & they will regret it & they will be defeated."
Prosecutors argued that these tweets indicate an attack on the Boston Marathon was on his mind a year before the bombings.
Tsarnaev attorney Miriam Conrad, who opted not to cross-examine the bombing survivors who testified during the first week of the trial, got Kimball to acknowledge that some of his information about the tweets came from other agents and that he didn't check them out for himself.
Conrad also established that some of the tweets appeared to be rap lyrics.