Defender Azpilicueta and forward Pulisic limped off during Chelsea’s 2-1 defeat by Arsenal in the FA Cup final on Saturday.
Chelsea will visit German champions Bayern Munich on 8 August, trailing 3-0 from the first leg of their last-16 tie.
“I don’t know the full extent of the injuries,” Lampard told reporters. “But I know the hamstrings with Azpi and Christian – they have to be scanned and assessed over the next few days.
“They clearly won’t be fit for next week.”
Lampard was also full of praise for match-winner Pierre-Emerick Aubameyang.
“He scores two goals, one being a penalty which he earned. We were very clear with the players that Arsenal play long balls in behind you, they play football as well,” he said.
“We allowed him in easily, he is a top-class player and the second goal is the sort of speed and quality from a player of his level – moments like that from Aubameyang obviously finish you off.”
Lampard was visibly unhappy with the decision to dismiss Mateo Kovacic for a second yellow card midway through the second half, saying he thought it was a penalty but that “it wasn’t a sending off, I think that was pretty clear.”
Although he seems certain to end his first season back at Chelsea without a trophy, Lampard insisted he has been pleased with his maiden campaign at Stamford Bridge.
“I can’t criticise the players in their approach or desire to win the game,” he added.
“We didn’t play well enough and we know that in our dressing room.
“We shouldn’t become too stuck on today. We need to look at the season as a whole, what we managed to do, where we came in the league.
“It was a good season for us and today would have been the icing on the cake.”
Reuters and PA