Using the Lexeme feature of Accordance I can quickly see that Matthew uses the verb ἐσπλαγχνίσθη verb in variant ways just five times. Nonetheless each has Jesus as its subject. There is something characteristic of this main character of this Greek gospel that this one Hellene phrase seems to convey particularly well.
It suggests Jesus feels something. There's a depth in the pit of his stomach. It's a profound inner gut movement in response to the physical and emotional needs of others. This affects his body, his passions.
The other canonical gospels use the Greek verb less frequently, Mark four times and Luke thrice, John never. The marked term is always in relation to Jesus only, either him as the subject or him telling a story where somebody (like him presumably) is the protagonist responding from the inside out to the predicament of somebody else in dire need, in deep pain.
Compassion is the Latin root English word that most Bible translators use to mirror this rare Greek characteristic of Jesus; and to make it verby, they have to use phrases like "was filled with compassion" and "was moved with compassion" and more actively "felt compassion" and more possessively "felt compassion." None of these is particularly bad at conveying the sense of the Greek verb.
But the verbing of the noun, and particularly of this noun, is an odd and rare thing to do. It's a linguistically marked thing to do. It focuses attention on Jesus in an active way. It makes a movie out of a snapshot.
The more common and unmarked phrase in the NT of course is τὰ σπλάγχνα. This is regularly used by Paul and by the gospel writers too. The plural is often translated by the KJV as "bowels." Our more contemporary English might prefer "guts." The older English gets at pathos as in empathy and in sympathy. Our newer English gets at bravery and at intuition. But the reason I'm bringing up the noun at all is because it's the default form in the Greek.
When Matthew says ἐσπλαγχνίσθη ἐπ’ αὐτοῖς he's not just saying "he was deeply moved by them." That's the best English translation I can find of the phrase. It's the one by Dr. Clarence Jordan. We could just as well in English describe this as Jesus's heart break, another metaphor illustrating the embodied incarnate profundity of dynamic change in this man. Nonetheless, Matthew's Greek is suggesting that Jesus was "gutted" by them. They were in such a sad state themselves that he was being disemboweled, unstomached by them perhaps.
The context of Matthew 14 makes this verbing of that stomach noun even more powerful because Jesus is trying to get away from these folks, trying to have a private moment of pain and grief all to himself since he'd just learned of the brutal murder of his own flesh and blood cousin and of the great preacher and baptizer John. What happens next, Matthew shows us, is that Jesus finally sees them. It completely wrecks him. They in their condition, how shall we read it? rip his guts out. That this is unique to Jesus in Matthew and in two other gospels.