England bowled Bangladesh out twice in consecutive sessions to seal a 2-0 series triumph, the touring side capitulating in their second innings to 123 all out and slipping to an innings defeat inside three days.
After rain wiped out the morning session, England made up for lost time by taking 10 wickets in 34.1 overs led by fast bowlers Steven Finn, who took five for 42, and James Anderson [ Images ] whose figures were three for 16.
"They were two crazy sessions," Strauss told a news conference as he sat next to England's man-of-the-series Finn.
"To finish the game like that was a nice way to wrap things up. It was a professional job.
"There was a lot that came out of these two games, like the performances of Steven Finn and Ajmal Shahzad and Eoin Morgan [ Images ] got two Tests under his belt, but we are realistic enough to know there are sterner tests to come," he added.
Pakistan are up next for England in a four-Test series starting in July and Strauss was relishing the examination they will provide before the Ashes series in Australia [ Images ].
"We want to face the best quality side from Pakistan as possible," Strauss said.
"That is better for Test cricket in general and Pakistan cricket. It is going to be a good test for us prior to the Ashes," he added.
Bangladesh coach Jamie Siddons, rarely shy to criticise his team when they have under-performed, praised the quality of England's bowling.
"The conditions and the swing were too much for us today and Swanny (Graeme Swann [ Images ]) bowled beautifully yesterday," Australian Siddons said.
"They bowled beautifully in both of those sessions. It was good Test bowling.
"But it was James Anderson who tore the heart out of us. Finny may have taken five in the end but it was Anderson who did the damage with his swing bowling. He would have taken wickets against any team in the world with that first spell, especially against left-handers," he added.