Crush them with what? They had just ended a century of disastrous wars against the Persian Empire and a terrible episode of the Black Plague. Islamic Expansion did not occur because Islamic Armies were unbeatable, Islamic Expansion was an expansion into a power vacuum at a point where the Persians and Byzantines were both so depopulated they were in economic shambles and could no longer patrol their own frontiers.

The plague initially struck in 540, late in Justinian's reign, in a town called Pelusium in Egypt. When it hit Constantinople it burned through the city for 4 months with a peak death rate of 10,000 a day. At one point bodies were tossed into an unused castle which was filled till they overtopped it's walls because there was no where to bury them, no one to bury them. This plague killed one quarter of the population of the Mediterranean basin. Justinian could no longer raise enough troops to protect his empire, invading Goths moved into the Italian peninsula and looked impossible to dislodge and Huns threatened to sack Constantinople. Justinian had nearly taken back control of the entire old border of the Roman empire, but the Byzantine Army that had numbered 500,000 early in his reign was whittled down to 150,000 by the end due to plague and decades of constant war. Justinian left an exhausted Empire behind when he died, bereft of men and leadership.

The Persians took advantage a few decades later. Between 610 and 619 they sacked Jerusalem, killing every male in the city, selling the women and children into slavery and worse yet (from the Byzantine perspective) carrying off the relic thought to be the one true cross, and they also sacked Egypt, the bread basket of the Byzantine Empire. The Balkans had been lost to Slavic invaders who were also overrunning Greece, so the Romans of Constantinople had to buy grain from Slavs in Thrace (a first for them, "free" bread and circuses had been a reality in Constantinople since Constantine had made it his capitol). A new Emperor named Heraclion threw back the Persians. He invaded at Issus (site of Alexanders victory) and defeated the main Persian army. He invaded Persia, and when the Persians bribed barbarians to attack Constantinople in his absence he ignored the threat, trusting Constantinople's defenses to hold and continued his invasion, sacking the Persian capitol at Ctesiphon and inflicting savage retribution for the sack of Jerusalem. Persia was broken utterly, but Byzantium was so damaged by the war burning through cities and farmland, and mass killings of soldiers, merchants and farmers that the economy was irrecoverably broken, and the military weakened to the point the Byzantines could no longer defend their borders.

622, the year Heraclius began his successful, but ultimately Pyrrhic invasion of Persia was the year the Islamic armies started their wave of conquest in the Arabian Peninsula. The Arabs were able to take the remnants of Persia easily (the Persians actually asked the Byzantines for help fighting this new menace, but the Byzantines at this point had no help to give). By 632 Islamic forces had begun crossing the Byzantine borders at will. The Byzantines had another great weakness: a confessional fight as old as Christianity itself. Dissident Christians in Alexandria, believing the Islamic Arabs would be more tolerant to their heretical views than Constantinople had invited the invaders in (to their great surprise Islam was far more brutal in suppressing competing faiths than the Roman Emperors ever were). please see comments for my retraction/correction/allowance I was overly aggressive in word choice in this parenthetical

The Byzantines, weakened by a truly awful century of plague, constant warfare, and doctrinal battles between the official state religion in Constantinople and dissidents who taught that Christ was not fully divine, and was a prophet to the one God had broken the Empire to the point it could no longer defend itself.

Constantinople itself would have been sacked and conquered, if not for a lucky invention in 672: Greek Fire. The Byzantines used it to destroy the Arab fleet attacking the city and saved their capitol, but Greek Fire was too little too late to protect the Levant and North Africa, all of which fell, virtually undefended, to invading Arabs. The Islamic/Arab forces had won numerous battles, that should not be ignored, but they were fighting in the ashes of two once powerful empires, the Persian and Byzantine Roman, who had only a fraction of the manpower and wealth they had once controlled. Add to that the religious disputes that were tearing the Byzantines apart from within and the Islamic conquest can be largely described as much an episode of walking into a once rich persons empty house and taking it by squatters rights as a conquest. There just weren't enough Persians and Greeks left to fight back at this point, and the ones there were were so poorly led they didn't put up much of a fight.

If you want a detailed break down of the period between the highwater mark of Byzantium under Justinian, the ensuing plague and wars against the Persians that bled the empire white and the Islamic invasions that conquered so much of the Middle East and North Africa a good start from the Byzantine side is Lost to the West by Lars Brownworth.