The Clarets came away from the London Stadium with a point after Wout Weghorst’s headed opener was cancelled out by Tomas Soucek – although Maxwel Cornet missed a penalty he won himself to make it 2-0.
Nick Pope also made two stunning stops to preserve a point late on.
But, 48 hours after the surprise sacking of Sean Dyche, the club appear no further down the line to appointing a permanent replacement, and Jackson will get on with the task as long as required, with another important game to come on Thursday against the Saints, before Wolves come to Turf Moor on Sunday.
Asked about his plans moving forward, Jackson said: “We will have a recovery day tomorrow (Monday) and go from there.
“I think, when it is ready to be said, which I don’t know, and I don’t know what is being discussed behind the scenes at this moment in time.
“But I am sure the board and chairman will give the information that supporters want.
“The priority is the next game for us and we have to concentrate on what is next.”
Check out the latest Premier League transfer speculation below...
1. Dendoncker wanted by Lazio
Lazio have reportedly added Wolves star Leander Dendoncker to their summer transfer wish list. (Corriere dello Sport) | Getty Images
2. Rudiger on Real radar
Real Madrid are assessing the possibility of signing Chelsea defender Antonio Rudiger on a free transfer. (ESPN) | Getty Images
3. Palace step up Aribo interest
Crystal Palace have reportedly intensified their pursuit of Rangers central midfielder Joe Aribo. (Football Insider) | Getty Images
4. Norwich want Davis
Norwich City have reignited their interest in Aston Villa striker Keinan Davis ahead of the summer. The striker could be sold for around £4m. (Football Insider) | Getty Images