The incidents are said to have taken place during their 2-2 group stage draw in Hungary on December 13.
They occurred just three days after four Chelsea fans were suspended by the club after claims they racially abused Manchester City forward Raheem Sterling during a Premier League clash at Stamford Bridge.
Chelsea reacted angrily at the time, releasing a statement denouncing those said to be involved.
It read: "Anti-Semitism and any kind of racial or religious hatred is abhorrent to this club and the overwhelming majority of our fans.
"It has no place at Chelsea or in any of our communities.
"Any individuals that can't summon the brainpower to comprehend this simple message and are found to have shamed the club by used using anti-Semitic or racist words or actions will face the strongest possible action from the club."
Punishments available to UEFA included the partial closure of Stamford Bridge for European games if Chelsea were found guilty. However, UEFA's Control, Ethics and Disciplinary Body confirmed on Thursday that proceedings against the west London club have been closed.
Chelsea chairman Bruce Buck responded to both incidents by greeting Chelsea fans at the turnstiles before their game against Brighton on December 16 to warn them against anti-social behaviour.
Steve Atkins, Chelsea's director of communications and public affairs, was also present at the Amex Stadium as the club’s hierarchy took decisive action to try and improve supporter behaviour.
In January, Chelsea launched a ‘Say No to Anti-Semitism’ scheme in an attempt to educate fans on anti-Semitism.
The campaign organised a trip for 150 people, who were a mixture of club staff, stewards and fans, to learn about the Holocaust with trips to Auschwitz and Birkenau concentration camps.
A number of Chelsea supporter groups also joined forces to form 'Chelsea Together', a group independent from the club with the aim of educating fans and eradicating racist and abusive behaviour.
The Portugal winger will be suspended for the next three UEFA competition matches for which he is eligible after being found guilty of "assaulting another player".