The former Pompey boss succeeded Sam Ricketts in the New Meadow hot seat last month after almost two years out of management.
But Cotterill's impact at the Shrews has been instant and they’re unbeaten in the three league games he’s taken charge of.
After draws with Accrington and Charlton, they delivered a 1-0 victory at Hull on Saturday. Charlie Daniels notched the only goal on 27 minutes.
Denver Hume: Portsmouth's expensive forgotten man and why former Sunderland defender really could be one for the future
'Real driving force... lion-hearted display... classy presence' - Neil Allen's Portsmouth ratings from 3-0 Carabao Cup win at Cardiff
Cardiff 0 Portsmouth 3: Neil Allen's verdict - From Fratton boos to 'Just like watching Brazil' as brilliant Blues produce remarkable cup shock
'We’ve got a real problem': Portsmouth boss reveals headache after career first at Cardiff
'We wanted to show him a bit of love' - Portsmouth-based Spurs fans' terrific gesture to ensure Dane Scarlett feels at home on the south-coast
Cotterill admitted it's been a 'whirlwind two weeks' in the Shrewsbury job.
And he toasted the success against the Tigers.
Speaking to the Shropshire Star, Cotterill said: ‘All of the staff, players, all players that haven't played, everybody, I thanked them for their efforts this week because it's been a whirlwind two weeks for me.
‘There isn't any time to take a breath so I thanked them then, which I think is important under all the emotions that'll be flying around at this moment.
‘But it's also important that we keep ourselves on an even keel.
‘To restrict Hull to no shots on target is quite an achievement.
‘I also think there were some golden opportunities to add to the one goal we scored.
‘We changed the system a little bit, on about 77 minutes, that slight tweak helped us. For Hull City not to get an effort on target we're absolutely delighted with that.
Hull welcome Pompey to the KCOM Stadium in front of the Sky Sports cameras on Friday evening (5.30pm).
And Grant McCann will demand a greater goalscoring threat when his troops face the Blues after they fired blank against Shrewsbury.
The Tigers boss told the club’s website: ‘We just didn’t test their keeper, which is really frustrating for everybody because we’ve been good on that front, in terms of the goals we have scored.
‘We’re always demanding more from the forwards, the midfielders, the full-backs, i.e. crosses and assists. We just didn’t do it and ultimately, we paid the price.
‘We knew what we were coming into – they’re an experienced group. They sat behind the ball a little bit and made it hard for us to try to break them down.’