He quickly tried to make up for that miss by attempting to play in Marcos Alonso, but there was slightly too much weight on his pass and Liverpool goalkeeper Alisson Becker was able to react quickly enough to make the save.
It was Pulisic who Lukaku looked for as half-time approached, but his flicked pass was easily cleared.
Within the first five minutes of the second period, Alonso pulled a shot wide from a Pulisic cross and then the former Borussia Dortmund star squandered another wonderful opportunity by sending a weak effort far too close to Alisson, who saved easily.
Like too many of Chelsea’s forwards, Pulisic is not clinical. He can score brilliant goals and produce moments of real promise, but few people would stake any real money on him hitting the back of the net when a big chance arrives.
Alisson did not even have to make a save from another good chance in the 68th minute, when Pulisic again sent his effort wide after being set up by James.
It appeared Tuchel might have run out of patience with his missed chances with five minutes of normal time remaining, when Pulisic’s number 10 was displayed as Hakim Ziyech prepared to go on.
But it transpired a mistake had been made and Pulisic’s number was replaced by that of Lukaku’s, who trudged his way off and Pulisic was moved into the middle to take up a false nine position.
There he remained Chelsea’s biggest threat, with his pace causing an issue for Liverpool’s high defensive line. It was a Trent Alexander-Arnold boot that prevented him from trying to turn in Ziyech’s cross in the first half of extra-time.
That proved to be Pulisic’s last sight of goal, as he was finally replaced by Ruben Loftus-Cheek for the second half of extra-time. He did not look particularly happy as he shook his head and stared back at the pitch from the bench, but father Mark cannot complain that his son had not been given more than enough time.