Kevin Nugent temporarily takes charge of his second game tonight following Jackett's departure as the Swans take on high-flyers Scunthorpe at home.
For the Swans, Britton remains sidelined with a dead-leg.
Tate is also struggling with a hip injury while Andy Robinson faces a late fitness test.
For Scunthorpe, Cliff Byrne and Joe Murphy are rated doubtful after they both required stitches last Saturday after a clash of heads during the game.
Ian Baraclough, Steve Torpey and Matt Sparrow are all fit again for the Iron.
Leaders Scunthorpe are top of the League, leading 2nd placed Oldham by 3 points.
They've won their last 3 games without conceding a goal, all at home.
Their last defeat was 11 games ago, Blackpool beat 3-1 in mid-December.
Scunthorpe captain Andy Crosby shared his thoughts ahead of tonight's game: 'Swansea are still in a good position in seventh so they are very much still in with a shout of getting into the top two.
'It is a club that demands Championship football. It has a big stadium, big fan-base, and they have spent a lot of money trying to get there.
'They came out of League Two with us and got into the play-offs at the end of last season.
'I think there is always a backlash when a manager leaves. Personally I am glad they have had a game for them to get that out of the way.
'The fans have been on their case a little bit which led to Kenny Jackett going, and hopefully we can take advantage.
'It is one of those games where we are playing somebody up there. We have won our last three games without conceding a goal, and we are on a great run away from home and hopefully it can continue.
'But Swansea is never an easy place to play, even though it's a great stadium. They have one or two individual players that could hurt us. It is well documented Trundle has got a lot of ability, natural ability let's say, and if you give him time he can really hurt you.
'But there's not only him, Andy Robinson for me is another good player, as is Leon Britton.
'But we have got our own players who can cause them problems.'
You can predict the score of tonight's game here
I think we'll do well to get another draw. My heart says 1-1 but my head thinks we'll narrowly lose.