Following their opening-day victory over Borussia Monchengladbach, the Bundesliga champions maintained their unbeaten start on Saturday thanks to Mandzukic's acrobatic finish from Thomas Muller's 13th-minute cross.
Frankfurt threatened an equaliser but were unable to penetrate the Bayern defence, with goalkeeper Manuel Neuer in particularly good form.
Guardiola felt the performance from his side was much improved from their opener, and he reserved special praise for the powers of recovery shown by his players following a busy week of international fixtures.
"Compared to last week, we controlled the game much better," the Bayern boss told the club's official website. "Against Gladbach we still allowed too many counter-attacks, which was better today.
"It is never easy after the international break, we only had three days. Nevertheless, we created a lot of opportunities.
"I am happy and satisfied 100 per cent. "
Bayern are now one of four teams with two wins out of two in the Bundesliga, while defeat leaves Frankfurt still searching for their first victory of the season at the foot of the table.
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