The 43-year-old made history by becoming the oldest man to ever play at a World Cup when he came on as a late substitute in Colombia’s 4-1 win over Japan on Tuesday.
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Mondragon, who is due to retire after the tournament in Brazil, praised Pekerman for encouraging him to keep playing international football and helping him to write his name into the history books.
"Jose Pekerman convinced me to continue playing. I will never forget that,” he said.
"If it wasn't for him, I would have retired two years ago.
"I feel privileged to be here, it was my best birthday ever."
Mondragon’s 85th-minute appearance against Japan also broke the record for most time elapsed between World Cup finals appearances, with the 43-year-old last featuring for Colombia 16 years ago at France '98.
The record was previously held by Switzerland's Alfred Bickel, who went 12 years between playing in the tournament when he featured in France 1938 before then appearing in 1950 in Brazil.