Blues came from a goal behind to earn a point against The Lions at the St. Andrew's Trillion Trophy StadiumBCFC
In a game, in which there was generally little to separate the sides, Millwall bagged their opener just after the hour-mark, before Chelsea loanee Clarke-Salter earned Blues their third successive draw with his 79th minute leveller.
On a bitterly cold afternoon, Blues had a least one clear-cut penalty decision go against them and they were also guilty of missing a couple of really decent chances.
There was just a solitary change to the Blues starting line-up from midweek, with Lukas Jutkiewicz coming in for Jeremie Bela.
Despite completing his three-match suspension, Harlee Dean had to be content with a place on the substitutes' bench.
With five minutes played, Jude Bellingham had to be alert to stop Jiri Skalak with a fine tackle on the edge of his own area, with the Millwall man about to burst through and unleash a shot.
Blues had half a shout for penalty when Bellingham appeared to be impeded inside the Millwall box by Murray Wallace, but referee Woolmer waved play-on.
Millwall broke with pace on the counter before the ball was swung in from the left flank towards Ben Thompson but he was unable to keep his header down as he powered it well over the bar.
Midway through the half there was disappointing sight of seeing Marc Roberts stretchered off with a leg brace after he had landed awkwardly during an aerial challenge with Matt Smith.
Dean stepped up to take his place in the centre of defence alongside Jake Clarke-Salter.
Blues fashioned their first attempt on goal just ahead of the half-hour mark when Ivan Sunjic tried his luck with a fierce drive from 25 yards, but Millwall 'keeper Bartosz Bialkowski dived at full stretch to his left and was able to push the ball away.
Lukas Jutkiewicz then met a cross from the left but it lacked power and was comfortably held by the Lions stopper.
Millwall would have taken the lead on 34 had it not been for a superb save by Connal Trueman.
Dan Crowley was robbed of the ball in his own half by Jed Wallace, before Wallace pushed on and sent in a pinpoint cross.
Smith rose well and met the ball with a fierce downward header, but Trueman was equal to it and got down brilliantly to get a hand to it and keep it out of the back of the net.
Blues were coming under a spell of real pressure and Trueman was called upon again minutes later to deny Ben Thompson with another neat save.
Deep into stoppage time at the end of the half Wallace should have done better for the visitors when a pass found him to the right of the Blues goal, but he skewed his shot across the front of the goal.
Half-time: Blues 0 Millwall 0
Within minutes of the restart Blues had a major shout for penalty turned down after Gimenez was clearly pulled back in the box by Cooper, but despite the protestations of the players and the home crowd, the referee decided that there was nothing doing.
Blues should have scored moments later when Jutkiewicz burst through, but under pressure and with just the goalkeeper to beat, the striker sidefooted his shot wide.
Blues made their second change of the match on 55 minutes when Jeremie Bela was sent on for Fran Villalba.
Clotet's side were continuing to probe forward, but a well-organised Millwall rear-guard was holding firm against them.
Very much against the run of play, Millwall took the lead on 61 minutes. Blues lost the ball midway inside the Millwall half.
The visitors burst forward with pace before Wallace laid the ball off to Shaun Williams in space 25 yards out.
Williams made a perfect connection with the ball and it flew past Trueman and into the top corner of the net.
Blues made their third and final change of the game on 65 when winger Jefferson Montero replaced Gimenez.
Blues showing plenty of endeavour as they looked to find a way back into the game, but far too often they were running into trouble or misplacing a pass at the vital moment.
But they were finally rewarded with a goal with just over 10 minutes of normal time remaining.
After winning a corner on the right, Crowley swung in a magnificent ball and Clarke-Salter rose majestically and headed it down and in past a flailing Bialkowski.
A minute later Blues went mightily close to taking the lead when Bellingham's well-worked attempt went inches wide of the post
That proved to be the final attempt on goal as the two sides played out the draw.
Blues: Trueman, Pedersen, Roberts (Dean, 26), Colin, Crowley, Jutkiewicz, Clarke-Salter, Villalba (Bela, 55), Bellingham, Gimenez (Montero, 65), Sunjic.
Subs (not used) Camp, McEachran, Maghoma, Davis.
Goals: Clarke-Salter (79).
Millwall: Bialkowski, M Wallace, Cooper, Williams, J Wallace, Thompson (O'Brien, 89), Smith (Bradshaw, 84), Romeo, Pearce: Molumby, Skala (Bodvarsson, 84).
Subs (not used): Steele, Brown, Mahoney, Mitchell.
Goals: Williams (61).
Referee: Andy Woolmer.
Attendance: 19,715 (1,182 Millwall fans)