Martino's men open their tournament against Paraguay on June 13 in La Serena, Chile, just seven days after the European club championship is decided in Berlin.
With six players in his current squad - set to play friendlies with El Salvador and Ecuador later in March - still in the hunt in the Champions League, Martino said the European governing body needed to take into account international competitions when planning their showpiece tournament.
Barcelona's Lionel Messi and Javier Mascherano, Paris Saint-Germain pair Ezequiel Lavezzi and Javier Pastore, and Juventus' Roberto Pereyra and Carlos Tevez are among those on track for the European final.
"We need to have the players from the first day and they are very keen to take part in the Copa America but they are also going to want to play the Champions League final after preparing all year," Martino told a news conference on Friday.
"It's going to be a tough decision, the fact I don't have to take it is because we haven't got there yet.
"It seems to me that little thought is given to the needs of what happens on this side of the world."
Martino pointed out the 100th holding of the Copa America would be granted more time between the European season finishing, and the South American showpiece starting - with the Copa reaching its milestone in 2016.
"I do not think next year [the Champions League final] will be played at the same time," Martino said.
"Now also it could have been avoided, it is a way to protect the players."
Martino recruited River Plate defender Ramiro Funes Mori to his squad, but the 23-year-old's form has been under scrutiny - something the Barcelona coach said he had no concerns with.
Mori has played three of five Argentinean Primera Division games this term, but is yet to help his side to a clean sheet - with River shipping six goals in those games.
Martino pointed to Mori's form last season as his reason for the call-up.
"From our side, [Mori] was never any doubt," Martino said, ahead of their first friendly with El Salvador in Washington on March 28.
Martino also hailed Messi's output against Manchester City on Wednesday, as he helped Barca into the last eight in Europe.
"I really can't think of a parallel with his performance in Wednesday's match," Martino said.
"It had been a long time since I'd seen one player be so absolutely decisive like Leo was in the return [leg] with City."
