"For the spectators it was a top game with high intensity," Flick said. "I am satisfied overall. It was a high-tempo game. We had them under control for the first hour and we could have scored a second goal.
"Still I have to praise my team because we played good football. We were fresh, had courage and played with confidence against a top team."
Both teams, who have qualified for the World Cup, had a handful of chances in a fast-paced first half, with Dutch striker Donyell Malen firing wide in the 35th after the Germans came close through Leroy Sane and Timo Werner.
Netherlands goalkeeper Mark Flekken was beaten on the stroke of half-time when Muller latched onto a free ball in the box and thundered in his 43rd international goal.
Germany's David Raum should have done better three minutes after the restart when Sane found him with a pinpoint pass but the midfielder sent his shot from in the box far over the bar.
The visitors were pressing high and controlled the pace of the game but the hosts struck against the run of play in the 68th when Bergwijn slotted in from close range after Denzel Dumfries had headed the ball on following a quick move.
The Netherlands were unlucky not to be given a penalty a few minutes later when Germany's Thilo Kehrer clearly felled Memphis Depay but the referee, having initially awarded a spot kick, changed his mind following a VAR review.
Germany came close again in the final minutes through Lukas Nmecha but the 23-year-old could not snatch a late winner despite a golden chance.