Callum Connelly’s 12th-minute header handed Joey Barton’s side a lead which they never looked like surrendering.
Having lost Ellis Harrison in the warm-up, prompting a reshuffle with Oli Hawkins recalled, the Blues struggled for creativity throughout.
The outcome was a Highbury Stadium loss which sees them drop to seventh – and outside the play-offs – in this congested promotion battle.
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Jackett said: ‘I didn’t think we really did enough in the first half.
‘I understand the elements played a big part, but didn’t think we had our usual sharpness, they were half a yard quicker to the ball and deserved their 1-0 lead at half-time.
‘Similarly, with the elements, I thought we could have a big second half and come back into the game.
‘I still felt it was there for us at half-time and was hoping with all off the pressure we had, and we had a lot, we would find more moments in front of goal.
‘Probably our best ones were Sean Raggett’s header headed off the line and a few moments of Marcus Harness travelling into the box with the ball, but we just couldn’t find that half a yard.
‘Ultimately they defended very well and protected their lead.’