Michael Vaughan praised England's outstanding performance to beat Bangladesh by an innings and 261 runs.
The England captain said: "It was a good start, good performance.
"Probably the only disappointment was the first 10 overs when were weren't quite at our best. But after that we were outstanding.
"We were pretty ruthless in the field and went on to get a big score in a positive manner which is how we've tried to play in the last year."
Vaughan was delighted to score a Test hundred at Lord's and said all the batsmen had played well.
And when asked if winning by such a margin was good for Test cricket, he added: "It's nothing the players can really worry about."
It was Trescothick's first hundred in a Test at Lord's and he was delighted his name would be etched there forever.
I met up with the guys on Monday and the enthusiasm and the buzz has been fantastic
He was awarded the Man of the Match and said: "It's been nice to get back into the environment and play Test cricket.
"I met up with the guys on Monday and the enthusiasm and the buzz has been fantastic."
Harmison took two wickets in two balls on the final day and was unlucky not to claim his first Test hat-trick when Anwar Hossain survived a strong lbw appeal.
The fast bowler said: "I must admit I didn't see much wrong with that to be honest. The umpire's got a hard job but I'm a bit disappointed as it would have been my second hat-trick in six weeks."
England now head to Durham for the final Test, which starts on Friday.
Harmison added: "It's my day on Friday to play at home. It will be a great occasion for me and my family."