Captain Azpilicueta pulled up with a hamstring injury five minutes after giving away a penalty that Pierre-Emerick Aubameyang converted to kickstart Arsenal's comeback.
And Pulisic, the scorer of Chelsea's early opener at Wembley, also made way four minutes into the second half with an identical issue sustained as he was charging through on goal.
Pedro then suffered a suspected dislocated shoulder late on and Frank Lampard has ruled the trio out of next Saturday's last-16 second leg with Bayern, which Chelsea will start trailing 3-0 on aggregate.
"I don't know the full extent of the injuries, but I know its the hamstrings with Azpi and Christian," he said at his post-match news conference.
"They have to be scanned and assessed over the next few days. They clearly won't be fit for next week."
Pedro, who was given oxygen as he was stretchered off the field, is expected to join Roma on a free transfer when his Chelsea contract expires later this month.
"I believe it could be a dislocated shoulder but don't go too soon on that," Lampard said when asked for an update on the forward's condition.
"I've not seen him yet as he was whisked away so it's a disappointing end as that's probably going to be his last game for Chelsea.
"He's been an incredible servant and I'm disappointed for him."
Chelsea got off to a flyer through Pulisic's fifth-minute strike but Aubameyang added to his penalty with an impressive second to take Arsenal's record tally of triumphs in the competition to 14.
The Blues' hopes of scoring an equalizer were dented by a controversial second yellow card shown to Mateo Kovacic for a challenge on Granit Xhaka.
Replays showed Kovacic barely made contact with his opponent and Lampard questioned referee Anthony Taylor's decision to reach into his back pocket.
"The penalty was rightly awarded, but it wasn't a sending off, that was pretty clear," he said.
And Lampard insisted on another day the outcome could have been different for Chelsea, who finished fourth in the Premier League in the club legend's first season in charge.
"Today was not about not showing up. We made a great start and had control of the game," he said.
"Then we got sloppy and got slower in our game and that changes the tone of it.
"If Christian goes through and scores instead of pulling his hamstring then things are different, although we didn't play well enough.
"I can't criticize the players and their approach in their desire to win this game. We can't be stuck on today - we have to look at the season."
Aubameyang ultimately proved the difference in the all-London final and Lampard admitted his side's defending could have been better on the day.
"He's scored two goals, one of those being a penalty which he earns," he said.
"I was clear with the players about the threat of Arsenal's long balls behind them. We allowed him in easily.
"Aubameyang's a top-class player. His second goal showed his ability. In moments like that Aubameyang can finish you off."