The Blues boss was forced to change a winning team for Saturday’s trip to the League Two leaders.
Clarke had performed alongside Christian Burgess in the previous week’s victory at Leyton Orient.
Yet with the 20-year-old sidelined, Tom Davies was recalled to the team for the clash with Plymouth Argyle.
Substitute Connor Smith’s 89th-minute strike prevented Cook’s men departing Devon with a well-deserved victory.
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
Portsmouth transfer news: The four Fratton Park departures Blues could still sanction before window shuts - including ex-Sheffield United defender and Luton midfielder
'We’ve got a real problem': Portsmouth boss reveals headache after career first at Cardiff
However, Pompey’s manager praised the contribution of the returning Davies.
He said: ‘I thought Tom Davies was excellent coming into the side.
‘Matt Clarke’s had a little bit of a thigh problem. We had it scanned on Friday afternoon and weren’t too happy with it.
‘He felt it at the end of the Reading game and felt it just before Orient yet ended up playing.
‘We have a good squad, you don’t risk players in games if you feel it’s not quite right, so others come in.
‘We’re not sure how long Matt will be out, it could be a week. We’ll see.’
Plymouth had taken the lead on 20 minutes when Yann Songo’o stooped to head home Graham Carey’s free-kick from the left.
Kyle Bennett levelled on 40 minutes, rifling home Conor Chaplin’s pull-back from the left-hand side.
It was the winger’s first goal of the season, capping an impressive display as he continues to re-establish himself in Cook’s side.
However, in the 87th minute, Danny Rose produced what appeared would be the Blues’ winner.
On as a 69th-minute substitute for Amine Linganzi, he controlled the ball on his chest before lashing in a 25-yard half-volley.
There was more drama to come, though with Smith popping up to grab a point at the death for Derek Adams’ side.
Cook added: ‘I’ve not seen Danny Rose do that in training, he wouldn’t be sub if I had!
‘It looked in, all the lads were saying so. We had good situations throughout and we have got to put some of our chances away from home.
‘But I was pleased with the lads. Our fans came away from Home Park knowing our players didn’t take a backwards step in the game and we showed we are a good football team.
‘I’m disappointed we didn’t get the victory, we should control the ball at those late stages, it is important for us.
‘Still, at the end of the day, we got a point and move onto the next game.’
– NEIL ALLEN