A 13th-minute strike from Mario Mandzukic proved the difference between the sides but Bayern were made to sweat until the final whistle after spurning a number of chances to kill the game off.
Bayern also had a few let-offs before celebrating their second successive Bundesliga win this season, with Eintracht unfortunate to have a goal disallowed before half-time and seeing a late penalty appeal turned down.
Despite that, Guardiola was pleased with the result, telling Sky television: "We controlled the game far better and let them have very, very few counter-attacks.
"We created many chances and wasted far too many of them, but I'm 100 per cent satisfied today [Saturday].
"I'm happy. We wanted a quick game, but it wasn't possible on this grass."
Meanwhile, goalkeeper Manuel Neuer welcomed the win, even if Bayern were made to work hard for it.
"We didn't want to come here and celebrate beautiful football, we came here to get our second Bundesliga win and we've done that," said the Germany number one.
Eintracht Frankfurt coach Armin Veh, however, was critical of the referee following the loss which left the Eagles rooted to the foot of the table after back-to-back defeats.
He was aggrieved that what appeared to be a valid goal from Alexander Meier on the stroke of half-time was disallowed for offside, while he also felt his side should have been given a penalty in the very last minute when Meier went down in the area.
"We scored a fair goal in the first half and he (the referee) really has to allow it," said Veh.
"In the end, there was a clear penalty too and I've just had another look at that."