After opening their World Cup campaign with a 2-1 victory over England, the Azzurri were the heavy favourites going into the game at Arena Pernambuco - even though their Central American opponents had upset Uruguay in their tournament opener.
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Motta had warned prior to the match that Costa Rica would be more accustomed to the playing conditions and he insists the Central Americans would have found life much tougher had the game kicked off later in the day.
"It's not an excuse, it's the truth," the midfielder told reporters after the game in Recife. "They managed to have great intensity, both with and without the ball.
"I don't know [if Italy would have won with a later kick-off] but it would have been different. If the climate was okay for everyone, like in Uruguay-England, where it was 14 degrees, we'd see a different game.
"Some of them are used to playing in this climate. They can play with more intensity and one saw that today [Friday].
"For example, in the game against England, we had the ball and they could not manage to do their high pressing, and when they had the ball, we could not manage to put pressure on them either.
"Today, instead, it was different. With all due respect to Costa Rica, they played a great game but, if you take them individually, they do not play for any of the big squads in Europe.
"Today we played at 13:00, in crazy heat. The secret is the climate. We can speak about attitude and many other things, but in my opinion the secret to their success was their great familiarity with this climate.
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Motta is concerned, though, that Italy will once again struggle to cope with the conditions against Oscar Tabarez's side in the clash in Natal.
"We know that it will not be easy against Uruguay, because they have a good squad and we will again play at 13:00," the Paris Saint-Germain star lamented.
"[The kick-off time] is strange and complicated, but we must recover and play a great game against them.
"Maybe they won't manage to play with the same intensity as Costa Rica.
"But we must forget this game [against Cost Rica] and try to see the things that we didn't do well, recover and face Uruguay like it's a final.
"If we win we're through to the last 16, so we will play with heart and give everything."
Italy need only a draw to progress to the knockout stage on account of their superior goal difference to Uruguay.