Chelsea’s German boss highlighted the importance of solidarity after the win at Burnley.
Fans on all sides at Turf Moor had stood to applaud before kick-off as part of a league-wide campaign to show support for Ukraine following the Russian invasion of the country.
But a number of Chelsea fans interrupted the applause to sing the name of their Russian owner Abramovich, who has announced he is looking to sell the Stamford Bridge club.
“It’s not the moment to do this,” Tuchel said. “If we show solidarity we show solidarity and we should do it together.
“We take the knee together. If an important person from our club or another club unfortunately dies we have a minute of respect.
“It is not the moment to give other messages. It’s the moment to show respect. We want to do this. As a club we need our fans to commit to this minute of applause.
“We do it for Ukraine and there is no second opinion about this situation. They have our thoughts and our support and we should stand together. It’s not the moment for other messages.”
Abramovich last week announced he was passing “stewardship and care” of the club to its charitable foundation amid calls from politicians for him to be the target of sanctions following the Russian invasion, then days later said he was seeking a buyer.
Chelsea have won 21 trophies, including two Champions League crowns and five Premier League titles, since the Russian took over in June 2003.
Following Saturday’s match, a Chelsea spokesperson said: “The club’s very firm view is that moments of respect or recognition should always be honoured by everyone present.”