England's 167-run win on the final day of the third Test saw them wrap up the four-match series 2-0.
And this crushing victory followed their second Test success at Old Trafford where England won by an innings and 120 runs inside three days.
"What we need to do is keep this team solid. We need not to panic. We've been outplayed by a better team and we need to work on our cricket, go back to the drawing board and get things right," Woolmer said after Tuesday's reverse.
"After Old Trafford some teams might have rolled over but we fought all the way through this Test match and conceded it this morning.
"I'd like to congratulate England. They've been better than us," said former England all-rounder Woolmer. "It's as simple as that and they are a good side on home territory, I've known that for years."
After England made 515, Pakistan responded with 538 featuring a stand of 363 between Younis Khan (173) and Mohammad Yousuf (192).
England captain Andrew Strauss's 116 was the centrepiece of the hosts England second innings 345 which left Pakistan needing 323 to win on the final day.
But a collapse, featuring the run out of Yousuf for just eight, saw Pakistan slump to 80 for five and they slid to 155 all out inside 48 overs.
For all of this series so far Pakistan have been without opening batsman Shoaib Malik because of an elbow injury and the lack of a solid first-wicket stand has left Pakistan's strong middle-order without a sound base.
"Guys have had the opportunity to go and make big scores. Shoaib Malik is a good opening batsman. He makes a difference up the order. We have to go back to the drawing board.
"I don't want to throw individuals out of my team. I want to make sure they get better. I will work with (openers) Salman Butt, Taufeeq Umar and Imran Farhat.
"But if they are not producing the goods it makes it very difficult for our middle-order which is very strong."
Pakistan have also been hampered by being without injured leading quicks Shoaib Akhtar, Mohammad Asif and Rana Naved.
Akhtar (ankle) and Asif (elbow) are in the process of regaining their fitness but Woolmer said he would not be rushing them back for the fourth and final Test starting at The Oval on August 17.
"There's no guarantee they will be ready. Shoaib Akhtar hasn't bowled (in international cricket) for six months and Mohammad Asif hasn't bowled for a month.
"Shoaib Akhtar is coming back at Shenley (where Pakistan have a two-day tour match against West Indies A next week).
"But to rush him back into a Test match at The Oval after six months of not bowling, any bowler would shudder at the thought if they were not fully fit."