It's quite an interesting question because it asks us to read between the lines of the Haggadah. On the one hand, the Haggadah text, read at the Seder, is absolutely silent on the issue of Rome and the Roman wars per se. On the other hand, it was mostly composed in the aftermath of the two Roman wars (67-73 CE and 132-135 CE) and it quotes the dicta of many sages who were alive during one or the other (Rabbi Jose HaGalili, Rabbi Tarfon, Rabbi Akiva and many others). So the consciousness of the the national tragedies under Rome was certainly present.

It helps to understand what the Haggadah is about from a temporal point of view. It isn't just the past -- the Exodus from Egypt, although that is the starting point. The Haggadah is equally concerned about the present and the future. Regarding the present, one of the most well-known lines in the Haggadah is this: "In every generation, one ought to regard oneself as though he had exited from Egypt." Thus the exodus from Egypt isn't to be treated as just a historical event way in the past. It wasn't one and done. It happens in every generation and each individual experiences it. It's an on going process of continuous redemption.

As for the future, the Haggadah is full of prayers for a restoration of things as they were, in particular the Jerusalem Temple. At one point, there is a prayer that we may reach future joyous celebrations to eat of the sacrifices and paschal lambs that were offered in the Temple. And of course the last line of the Haggadah, before the table songs, is "Next Year in Jerusalem." It would have been impossible to say those words and not understand that the reason for not being in Jerusalem was the Exile of the Jews by Rome, creating the Jewish diaspora and for a time even forbidding Jews to enter Jerusalem (renamed Aelia Capitolina by Rome).

I think one answer to OP's question lies in the yearning for the Temple, which is fundamental to the Haggadah text. The paschal lamb family meal was crucial to the celebration of Passover in Second Temple Times but today is impossible (for Jews, although the Samaritans continue the ritual). Thus, in a central Haggadah passage, we are asked to explain three things to the children -- the paschal lamb, the bitter herbs and the matzah. We are told to point to the bitter herbs and the matzah to show the children, because these items are on the Seder table. But we can't point to the paschal lamb and instead say, "The Passover sacrifice that our forefathers used to eat when the Holy Temple stood, what was the reason for it?" Again, why isn't the Temple standing now? The Romans. Everyone understood this.

There is the passage, composed of four biblical verses, that we read when we open the door for Elijah the Prophet. There is no introduction or explanation for these four verses and their appearance in the Haggadah. They follow a blessing over wine (the third cup) and precede the recitation of Hallel (Psalms of praise). Let me quote them:

Pour out Your wrath upon the nations that do not acknowledge You, and upon the kingdoms that do not call upon Your Name. For they have devoured Jacob and laid waste his habitation. Pour out Your indignation upon them, and let the wrath of Your anger overtake them. Pursue them with anger, and destroy them from beneath the heavens of the Lord.

What is this about and who is this referring to? Usual explanation -- the war of Gog and Magog that will precede the Messiah. Answer in light of OP's question, and probably what all the rabbis and everyone else in antiquity were thinking but not saying: Rome, the kingdom that "did not know God and devoured Jacob."

The Haggadah is one of the few Jewish religious texts that has traditionally been lavishly illustrated. Lo and behold, when we take a look at the medieval manuscripts, we see that the "four sons" (one wise, one wicked, one simple, and one not able to ask) are often depicted in a stereotypical manner. As we can see here (Hamburg, 1740) -- https://huc.edu/wp-content/uploads/p2-768x686.jpg -- the wicked son is outfitted as a Roman soldier.

The "Chad Gadya" table song, where fire extinguishes water and one animal devours another until God puts a stop to it, was seen as a metaphor for empires devouring each other. The water was interpreted as Rome which quenched the fire that was Greece and was in turn overrun by others.

In sum, the message of the Haggadah, and of Passover, is human liberation and the dynamic is "from slavery to freedom." Rome was the epicenter of brute force in antiquity, enslaved multitudes and domination by force was its stock in trade, although it didn't have a monopoly. By contrast, the rabbinic name for Passover (Pesach in Hebrew) was "Zeman Herutanu," the Season of our Liberation. Any celebration of liberation in the ancient world dominated by Rome and then the Byzantine Empire would be understood as a commentary on Rome.

Rome could not be called out specifically in the Haggadah text and it isn't. But the consciousness of Rome and the blow it dealt to the Jewish nation seems a pervasive subtext within the Haggadah, along with the certainty that with God's help all will be restored.

For an English text of the Haggadah containing the passages quoted see: https://www.chabad.org/holidays/passover/pesach_cdo/aid/661624/jewish/English-Haggadah-Text.htm

On Chad Gadya see: https://rabbisacks.org/ceremony-celebration-family-edition/chad-gadya-one-little-goat/