I wonder if this is "A Matter of Magnitude" by Al Sevcik. It is available on Project Gutenberg, so that at least matches.
In the story the gigantic human ship is menaced by an unknown alien ship they can't detect, so the human ship flees thinking the aliens must be too advanced to confront.
Big Joe (as she is known) is a damn Big Ship:
"She's a mighty big ship, Rogers," he said proudly to the navigator, ignoring the latter's rather vacant stare and fixed smile. "More than a mile long, and wider than hell."
[...]
Heselton smiled modestly and noted that Big Joe was undisputedly the largest, most powerful, most feared, and most effective spaceship in the known universe.
They get a signal from a nearby ship they can't see:
"Sir," another voice chimed in, "this is fire control. We've got our directional antennas on the thing. It's either directly right or directly left of the ship, matching speed with us exactly."
"Either to our right or left?"
"That's the best we can do, sir, without radar help."
"Admiral, sir," the lieutenant who had first reported the signal came running back. "Judging from the frequency and strength, we think it's probably less than a hundred miles away."
"Less than a hundr..."
Once the aliens realize the Earth ship can't see them they find it hilarious, and they threaten the Earth ship:
The alien's face, still smirking, appeared again on the screen. "He says," said the interpreter, "that he finds the presence of our armed ship very annoying."
Heselton knew what he had to do. "Tell him," he said, swallowing hard, "that we apologize. This part of the galaxy is strange to us."
"He says he is contemplating blasting us out of the sky."
The Earth ship, unable to fight what it can't see, retreats, but finally the scientists figure out what was going on:
"Look, sir," the professor gasped for breath. "We thought this was a spot on the negative, but one of the men got curious and enlarged it about a hundred times." He held up one of the photos. It showed a small, fuzzy, but unmistakable spaceship. "No wonder we couldn't spot it with our instruments."
Heselton snatched it out of his hand. "I see what you mean. This ship must have been thousands of miles..."
The professor shook his head. "No, sir. As a matter of fact, it was quite close by."
"But..."
"We figure that the total length of the alien ship was roughly an inch and a half."