Yaaras Dvash explains that we primarily mourn the destruction of the first Beis HaMikdash. The second Beis HaMikdash was a respite, a break in the long galus, but the primary destruction was the first one.
The Mabit (Beis Elokim, Shaar HaTefillah ch.17) writes, "When people of the later generations daven for Moshiach, it is more likely that their tefillos will be answered. Their tefillos have greater potential than the tefillos of generations before them." He explains that the later generations are closer to the time of the geulah, so our tefillos have greater potential to be answered. Furthermore, all tefillos of the past two thousand years are still present, waiting to be answered. Their tefillos join with our tefillos. So, it isn't solely our tefillos but the tefillos of all the generations that come together and go up before Hashem.
Yaaras Dvash (Drush 5) teaches that the first Beis HaMikdash was destroyed because people weren't davening. As it states (Tehillim 14:4), קראו לא 'ה, "They didn't pray to Hashem." Another source is the pasuk (Eichah 1:2), ודמעתה לחיה על, "Her tears are on her cheek." This pasuk can also be read, "Her tears are because of her cheek." The tears of the Churban came because of the 'cheek,' which represents tefillah (see Chulin 134:). This means the bitter Churban was לחיה על because people didn't daven. They didn't daven that the Churban shouldn't occur.
The Midrash (Yalkut Shimoni Yirmiyahu 327) says that when the Jewish nation was בבל נהרות על, on the banks of the Babylon River, en route to galus, Yirmiyahu left them, and everyone began to cry bitterly. They said, "Rabbeinu Yirmiyahu! Will you leave us?" Yirmiyahu told them, "I testify by heaven and earth that if you had cried just once when you lived in Yerushalayim, you wouldn't have been sent into exile."
The Midrash (Eichah Rabba 5:5) states, "The evil Nevuchadnezzar told Nevuzaradan, 'Their G-d accepts teshuvah. If they pray, Hashem will save them. Therefore, don't let them stop walking [when you lead them into galus], not even for a moment, so they won't have the peace of mind to call out to Hashem.'" Nevuzaradan followed Nevuchadnezzar's advice, and he didn't let them rest. His soldiers cut off the limbs of anyone who stopped walking.
So, we see that even Nevuchadnezzar harasha understood the power of tefillah. Their tefillos could have prevented them from going to galus. Also, the second Beis HaMikdash was destroyed because Yidden didn't daven. If they had davened, they could have prevented the Churban.
Chazal (Taanis 29) teach, "When the first Beis HaMikdash was destroyed, it was erev Tisha b'Av, Motzei Shabbos. The Levi'im were singing shirah. They were up to the words (Tehillim 94:23), אלקינו 'ה יצמיתם, 'Hashem will destroy them' (the Babylonians), but they hadn’t yet said those words, and that's when the goyim seized the Beis HaMikdash. The same happened by the second Beis HaMikdash." The Levi'im were up to the words 'ה יצמיתם אלקינו, "Hashem will destroy them" (this time, referring to the Romans), and before they could say these words, the goyim seized and destroyed the Beis HaMikdash. It seems that had the Levi'im said אלקינו 'ה יצמיתם, "Hashem will destroy them," the two Batei Mikdash wouldn't have been destroyed. Their tefillos would have probably prevented the Churban.
The Mesilas Yesharim (19) writes, "If a person will ask, who am I, and how am I important, that I should daven for [the gathering of] the galus and for Yerushalayim? Could it be that because of my tefillah, the galus will end, and the redemption will sprout? The answer is, as Chazal (Sanhedrin 37.) state, man was created alone, so each person will say, 'The world was created for me.' Hashem has pleasure when His children pray for this matter. Even if the prayers won't be answered (because the time hasn't come yet or for some other reason), they did their share, and Hakadosh Baruch Hu is happy with them. We are obligated to pray, and we shouldn't refrain because we don't have the strength. As Chazal (Avos 2) say, ואי לגמור המלאכה עליך לא הימנה לפטר חורין בן אתה, 'You are not obligated to finish, but you don't have the right to refrain...'"
Everyone must do his share towards bringing Moshiach. And when one does whatever he can, Hashem helps him.
