Jack Tucker’s seventh-minute goal has given Gillingham a 1-0 half-time lead over the Blues at half-time in Paul Cook’s first game in charge.
Josh Harrop started in place of Alan Judge in an otherwise unchanged Town line-up.
Judge was missing from the 18 due to a family bereavement and the team wore black armbands on their light blue away strip as a mark of respect.
The Blues set up in the same system as employed in their last four games with former Gill Tomas Holy in goal.
Skipper Luke Chambers was at right-back as he entered the top 10 of Town’s all-time appearance makers, Myles Kenlock at left-back with Toto Nsiala and James Wilson the centre-halves.
In midfield, Andre Dozzell and Teddy Bishop continued as the central two with Harrop a direct replacement for Judge on the left with Keanan Bennetts on the right. Parrott was in the number 10 role behind lone out-and-out striker James Norwood.
Jackson was back in the 18 for the first time since his sending off against Sunderland and exile to the U23s under former manager Paul Lambert. Luke Woolfenden also returned to the matchday squad.
Gillingham were unchanged from their 1-1 home draw with the MK Dons on Tuesday evening with former Blues loanee Jordan Graham and one-time Town academy youngster Stuart O’Keefe in their starting line-up.
The home side took the lead in the seventh minute from the game’s first serious attack. Dozzell fouled Graham not far outside the area to the right and Tom O’Connor lifted a ball into the area which was nodded on to the back post by Robbie Cundy from where Tucker smashed his first ever league goal past Holy.
The home side continued to look the more dangerous team and in the 11th minute keeper Jack Bonham’s long ball forward was flicked towards goal by Cundy but without enough power to trouble Holy.
Three minutes later the Gills felt they should have been awarded a penalty when Kenlock and Graham tangled as the winger tried to bring the ball in from the right.
Home manager Steve Evans and his assistant Paul Raynor, already constantly vocal towards the officials in any case, made that point forcefully towards the referee, his assistant and the fourth official. Town manager Cook had a quieter word with the fourth official, presumably to enquire whether Kenlock had been fouled.
O’Connor’s free-kick was blocked by Dozzell before the ball was blazed over by skipper Kyle Dempsey from the edge of the box.
Gillingham were very close to doubling their lead in the 19th minute when Olly Lee struck an effort on the turn which slammed against the foot of the post and away to safety.
Town were struggling to get into the game with too many battles being won by the more physical Gills.
However, in the 24th minute, Norwood drilled a bouncing ball over from the left and it fell to Harrop, who took a touch before hitting a strike which cannoned off a defender.
The Blues started to settle down and began get their passing going for a spell and in the 29th minute Parrott came very close to a leveller. After a long spell of Blues possession, Bennetts worked himself space on the right and crossed for Parrott, whose brilliant overhead kick struck the outside of the post.
The on-loan Tottenham man rued his bad luck as he continued his wait for his first senior goal.
Town should have been back on terms in the 39th minute when Harrop’s ball over the top beat Tucker and sent Norwood away on goal. The striker took the ball into the area but just as he was pulling the trigger, the Gillingham defender got back to slide in and block. Norwood will feel he shouldn’t have waited so long to shoot.
Two minutes into injury time Harrop curled a free-kick into the wall after Parrott had been fouled and moments later referee Graham Salisbury brought the half to an end.
Aside from the spell in which Parrott hit the post, the Blues had been disappointing having been unable to impose their game on the more frantic, direct approach taken by the Gills.
However, they ought to have been on terms with Parrott unlucky and Norwood having spurned the best opportunity when through one-on-one.
Town need to show more patience and not be drawn into playing the Gills’ game in the second half.
Gillingham: Bonham, Jackson, Cundy, Tucker, Ogilvie, O'Keefe, Dempsey (c), Graham, Lee, O'Connor, Oliver. Subs: Bastien, Johnson, MacDonald, McKenzie, Akinde, Willock, Morton.
Town: Holy, Chambers (c), Nsiala, Wilson, Kenlock, Dozzell, Bishop, Bennetts, Harrop, Parrott, Norwood. Subs: Cornell, Woolfenden, Ward, Downes, Edwards, Sears, Jackson. Referee: Graham Salisbury (Lancashire).