The draw means qualification from Group C is in Costa Rica's own hands and the final round of group matches looms.
It will not be plain sailing for Guimaraes, as his side's final game is against Brazil.
But the coach said his side's performance against Turkey filled him with hope.
"The big, big factor today was our character. We played very hard," he said.
"We didn't think about our opponents and we played our own game.
"My team played a beautiful game with so much power and we were very aggressive and attacked and I am very proud of my team.
Guimaraes said he was excited about the prospect of meeting the four-times winners in his next game.
"It will be an interesting game because it is the game that every player wants during their career," he said.
"With four points we are in a good position and we are going to do our best to get at least another point so we can make the second round.
"We know we have worked very hard to get here and we are going to do the best we can."
"We have four points and we are in a good position and we are going to do our best to get at least another point to make the second phase."
Goal hero Parks said divine intervention had a part to play in his strike.
"We were always ready so we were able to get the goal," he said.
"When I received the ball I felt very calm and because I believe in God I was able to score.
"Personally for me it was a great experience to score in a World Cup match and I dedicate it to my family and my girlfriend."