After nearly two decades in charge of the Blues, Abramovich has put Chelsea up for sale after he was linked with Russian president Vladimir Putin, who is behind the war in Ukraine.
Before kick-off at Turf Moor, there was a minute applause for victims of the war in Ukraine as a show of solidarity but the away fans could be heard chanting their Russian billionaire's name throughout.
Tuchel feels it was not the time to show affinity to the club's owner but to show solidarity with the people of Ukraine.
"It's not the moment to do this [chant Abramovich's name]," the 48-year-old said.
"Listen, if we show solidarity, we show solidarity, and we should do it together.
"We take the knee together and if an important person from our club or another club unfortunately dies, we show a minute of respect. It's not the moment to give other messages. It's the moment to show respect.
"We do this because this is what we are also as a club. We show respect as a club and we need our fans to commit to this minute of applause.
"At this moment, we do it for Ukraine and there is no second opinion about the situation there. They have our thoughts and our support.
"We should stand together as a club. It's not the moment for other messages."
On the pitch, Chelsea defeated Burnley 4-0 to tighten their grip on third position thanks to goals from Reece James, Christian Pulisic and a Kai Havertz brace.
