Chris Taylor's second-half goal secured a 1-1 draw which leaves Jackett's side five points above the bottom three with just one Championship game remaining before their FA Cup semi-final with Wigan.
And the manager afterwards admitted he had his concerns about his side's ability to cope with the dual demands of a Cup run and a survival scrap.
He said: "Since the quarter-final game it has been danger signals for me as manager - we could still be sucked into a relegation battle because we are focused on Wembley.
"It is in our own hands. We have games in hand. With five of the seven at home we have to take full advantage of this situation, although I know our home form has not been great this season.
"Since the quarter-finals we have played four games. Three have been away and we have won two and drawn two. So it has been a good response from the players."
The main talking point at St Andrew's was a first-half Richard Chaplow goal which was eventually disallowed for offside after referee Keith Hill twice changed his mind.
Jackett said: "The officials made four different decisions in about 30 seconds but I do think they made the right decision in the end.
"It was an offside goal. That is the bottom line. So in the referee's defence he did get it right."