Ivanovic scored his 34th Chelsea goal on his 377th appearance, amid suggestions his nine-year stay at Stamford Bridge could come to an end before Tuesday's transfer deadline.
The Serbia right-back, 33 next month and out of contract at the end of the season, has not made a Premier League start since September.
"When one player has the habit to play every game and it happens that you are not playing regularly, it's not easy to accept this decision," Conte said.
"Ivan knows well the situation and I'm pleased if he remains here, if he stays with us.
"But in this situation, for sure, the player must make the best decision for him, for his family.
"Ivan deserves great respect for his career at Chelsea
He played a lot of games, he won a lot with this team
"I think we have to respect every decision."
Conte, whose side next play at Liverpool and at home to Arsenal in the Premier League, declined to answer when asked if Ivanovic had requested a move.
He added: "I don't like to speak about my relationship with my players
I prefer to keep my conversations not secret, but private."
Goalkeeper Asmir Begovic made a number of key interventions to frustrate Brentford.
Begovic, back-up to Thibaut Courtois, will be allowed to leave for Bournemouth if Conte can identify a replacement
So far that has not proved possible.
"It's not easy," Conte said
"There are three days to finish this transfer window
"We have some situations
We are seeing, but we are not close (to replacing Begovic)."
Conte made nine changes and saw a Willian free-kick and Pedro strike take the Blues 2-0 up after 21 minutes.
Ivanovic struck the third and Michy Batshuayi converted a late penalty, with the only potential problem Willian's departure in the second half after earlier holding his ankle.
The Italian had described the FA Cup as an opportunity and he believes his squad players seized it.
Kenedy will be part of the squad for the second half of the season after coming off the bench as he now cannot be loaned out again, having already played for Watford.
"It was very important to see the right reply of these players," Conte added.
"Now it's important to move our concentration, our focus, on the league on Tuesday
We know against Liverpool it will be a very tough game."
Liverpool may be out of the FA Cup after a loss to Wolves earlier on Saturday, but Conte will not rule Jurgen Klopp's men out of the Premier League title race.
He said: "It's an important game
(But) after this game there will be 15 games to finish the season - if you win or you draw or you lose, it doesn't change a lot.
"We want to continue in this way, to keep them in the right distance.
"They are very strong
Liverpool is a team that can fight until the end to win the title."
For the first time in four weeks, Brentford fielded striker Scott Hogan, who came off the substitutes' bench but could not turn the match in his side's favour.
Hogan has been linked with West Ham but no club has met his Â£15million valuation yet and his future could be decided before Tuesday night, when the Bees play Aston Villa.
Brentford head coach Dean Smith said: "We fear (a renewed bid for Hogan) all the time
Whether it happens or not, I don't know.
"I'm thinking already about Aston Villa on Tuesday night and Scott's in those plans.
"He's got a valuation which hasn't been met
Until it is then he'll remain a Brentford player."
Smith was frustrated by the final scoreline, adding: "They probably didn't deserve that
The difference was the quality of the finishing."
Source : PA