Prolific Borussia Dortmund goalscorer Barrios, born in Buenos Aires to a Paraguayan mother, obtained Paraguayan nationality last month and scored on his debut in Tuesday's 2-1 World Cup warm-up loss to Ireland.
Midfielders Jonathan Santana of VfL Wolfsburg and Nestor Ortigoza, who plays for Argentinos Juniors in the country of his birth, are also naturalised Paraguayans and Santa Cruz said his team mates had no problem with their inclusion in the squad.
"Historically, we had some problems with wars with Argentina and in the football world, if you were to choose a game that you would change anything for a win, that's Argentina," Santa Cruz told a small number of reporters after the defeat to Ireland.
"It's always going to be a part of those people who are against it. But as players, we know how hard a player has to work to get into a national team and they are very welcome to play with us."
Barrios was picked to reinforce a forward line that despite being deprived of key striker Salvador Cabanas, recovering from being shot in the head in a Mexico City bar argument in January, contains plenty of options.
Paraguay could afford to face Ireland without Barrios' fellow Dortmund forward Nelson Haedo Valdez and Benfica's Oscar Cardozo - top scorer in the Portuguese league this season - allowing Rodolfo Gamarra to impress on just his third cap.
However, Paraguay's most experienced striker Santa Cruz says they cannot quite compete with an Argentine crop of forwards that had no space for Barrios who scored 19 goals in his debut Bundesliga season.
"I think that Argentina are one of those countries that are blessed, they have (Diego) Milito, (Gonzalo) Higuain, (Carlos) Tevez, (Lionel) Messi. I don't think they'll miss anyone. If Higuan wanted to play for our national team I don't think they'd miss him," the lanky striker said.
Paraguay were sluggish on Tuesday but Santa Cruz said he thought the team did a pretty good and that with Group F matches against Slovakia, New Zealand and holders Italy ahead, a run out against an Irish side who almost made the finals was useful.
The Manchester City striker, who has struggled with a knee injury since joining the club last year, added that he was feeling good and looking forward to the remaining warm-up games against South Africa-bound Ivory Coast and Greece.
"I feel really good in terms of the knee. I'm very happy and pleased that it has let me play and train regularly.
"We have two more games before the World Cup starts so I'm very confident I'm going to get in the best rhythm possible."
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