The 21-year-old linked up with the Blues in the summer transfer window after completing a switch from Borussia Dortmund that was arranged back in January.
Chelsea FC were widely reported to have shelled out around £58m to land the USA international but he has thus far not made much of an impact at Stamford Bridge.
Pulisic has found himself further down the pecking order at Stamford Bridge than he would like and he has only started three Premier League games so far this term.
Lampard has now delivered an update for Chelsea FC fans about Pulisic and he has warned Blues supporters to be patient with the young attacker as he adapts to life in England.
Speaking in an interview quoted by the Daily Mirror, Lampard said: “One of my problems in this job is that I have good players and everyone has their story – Christian has a price-tag, Ross Barkley is an international player, so too is Mason Mount.
“Callum Hudson-Odoi has just signed a new contract, Bayern Munich wanted to buy him, he is an international player, Ruben Loftus-Cheek will come back and be an international player… and I can’t pick them all in the game, unfortunately.
“All I have to demand of them is that they show me in training or show me in the game, when they get the chances to play, that they are worthy of their place.
“I spoke to Christian two days before the Grimsby game and was very clear about the standards. And we have to give him the fact he has moved country, leagues and is as young as all the young players we are talking about.
“He has just turned 21. So if anyone is getting too excited about this, they should calm down, frankly, because he has already started five games for us.
“What he needs to do is work daily, and work to show within the group that he deserves to play – as all the players do.
“I’ve been really pleased with Callum’s response to criticism and that has to continue.
“We can all focus on Pulisic, but Callum’s the same. I have to speak in the real world when I speak to them.”
Chelsea FC will return to Premier League action after the international break when they take on Newcastle United at home on Saturday 19 October.
The west London side are aiming to maintain their place in the top four this season after they finished third and won the Europa League under Maurizio Sarri last term.
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