Last season's Premier League runners-up want a replacement for Argentina forward Carlos Tevez who has joined Juventus and their performance in Pretoria in the first of two matches in South Africa highlighted the need for attacking reinforcements.
"We are aware that we need two or three more players," Chilean Pellegrini told a news conference after the defeat in the friendly at Loftus Versfeld.
"It's important to have a very good squad. I said before we came to South Africa that we need two players for each position and that's what we are looking for and I'm sure we will get them.
"It's difficult to say exactly which day but before the end of the month we will have a new attacker."
City, who finished 11 points behind Premier League champions Manchester United last term, have already bolstered their squad with the signings of Brazil midfielder Fernandinho and Spain winger Jesus Navas but they still have more shopping to do.
"We are working hard on new acquisitions before the start of the new season but we are not in an immediate hurry to bring them on board," said Pellegrini, who joined the club last month after the sacking of Roberto Mancini.
Sunday's match came less than a week after City's players reported back from their summer holidays with Pellegrini fielding two different sides in each half.
The English club play a second game in South Africa on Thursday, against AmaZulu in Durban, before heading to Hong Kong for a four-team tournament as they continue their build-up to the start of the Premier League season in mid-August.