The European champions comfortably overcame CSKA Moscow 3-1 in Russia courtesy of goals from Arjen Robben, Mario Gotze and Thomas Muller to surpass the record set by Barcelona in 2002-03.
In passing the milestone, Bayern added another entry to their long list of achievements, and Guardiola believes that the Bavarians have set the benchmark in fine style.
He said: "I'm very proud, especially because we secured these victories in such a dominant fashion.
"Ten consecutive victories in Europe is very special. It wasn't an easy game today, but the team reacted well.
"This showed what great character the team has. There are no excuses at a club like Bayern, you always have to play well."
Robben was keen to stress that records were not at the forefront of Bayern's thoughts, but he believes that the calibre of opposition makes it an extra special achievement.
The Dutchman added: "We have often said that we don’t play for these records, we play to win titles.
"But we have a great team and I’m proud to be part of it.
"It's a fantastic achievement to win 10 consecutive games in Europe, especially if you consider that we also played Barcelona and then Dortmund in the final (last year) on the way."
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