City made nine changes and fielded six teenagers - five of them making their full debuts - in the 5-1 defeat at Chelsea, who next play Everton in the quarter-finals.
Pellegrini's men face Dynamo in the Champions League last-16 first leg on Thursday (AEDT) and take on Liverpool in the Capital One Cup final on Monday (AEDT), so the City boss delivered on his promise to make wholesale changes.
"We are forced to do it," he said on BBC1, adding: "I think that if we play on Saturday it's better for us because we have to play for England in the Champions League."
Pellegrini denied disrespecting the FA Cup.
"If one team respects all the cups, it's this team," the Chilean added.
"That's why we are in the final of the Capital One Cup, that's why we won the two previous games in this cup. (At Chelsea) we couldn't because I think we have more important things at this moment."
Pressed on why the FA Cup was considered less of a priority than Europe, Pellegrini added: "It's not more important.
"I don't think I need to defend (the selection). The FA Cup, yes, of course (is special). (But) we have at this moment seven players injured. It's impossible for us to take the risk to play in both competitions.
"We have an option for the first time in our club to try to reach the quarter-final of the Champions League. With 13 players (available), not to prioritise (the FA Cup), it's a sensible decision."
City have now lost three straight games, after defeats to Leicester and Tottenham dented their Premier League title hopes.
Just 90 seconds after going behind to Diego Costa's opener, City equalised through David Faupala - one of the five full debutants - and it was 1-1 at half-time before Chelsea's second-half blitz.
Willian and Gary Cahill scored within eight minutes of the restart, and Eden Hazard and substitute Bertrand Traore added goals.
Chelsea also had a penalty, but Oscar's effort was saved by Willy Caballero.
The FA Cup has come under scrutiny which will only continue after Pellegrini's selection. Chelsea interim boss Guus Hiddink insists the competition must be treasured.
"Winning the FA Cup is beautiful. We must be careful not to devalue this," said Hiddink, who won the trophy with Chelsea in 2009, beating Everton in the final, and has a 100 per cent record from six games in the competition.
With the Blues languishing in 12th place in the Premier League, the FA Cup and Champions League are now Hiddink's priority.
"There's not much left in the league for Chelsea, to be honest," the Dutchman said.
Chelsea vowed to support any criminal prosecution and ban any supporter found responsible of coin-throwing after objects were hurled towards City players celebrating Faupala's equaliser.
A man was arrested after allegedly throwing a lighter on to the pitch, the Metropolitan Police said on Sunday evening, as enquiries continued.
A Chelsea spokesman said: "We condemn such idiotic and dangerous behaviour and if we can identify those responsible then we will ban them from Stamford Bridge."