Rachel Williams broke the deadlock in the West Country on two minutes but after Bristol Academy Women surged ahead via goals from Laura Del Rio and Angharad James, Jade Moore salvaged a vital point in the second-half.
Anything but a defeat at home to title winners Arsenal Ladies next Sunday (October 7) and a huge goal difference swing with third-placed Everton Ladies, will see David Parker’s charges book their place in Europe.
And with a 2-0 lead to take to Verona for the second leg of their Champions League opener on Wednesday – and a Continental Cup final against the Gunners also on the horizon – Carney knows the big games will keep on coming for Blues.
“It’s been a hectic few weeks for us with games coming thick and fast – and that will continue to be the case,” said the England international.
“We can’t blame our recent schedule for the fact we failed to perform as we would have liked against Bristol, although they are a difficult side to play against.
“I won’t take runners-up spot for granted until it is mathematically certain, and now we have to focus on the long trip to Verona before our two games against Arsenal.”
Williams gave the visitors an early lead following a corner when she first headed against the bar but reacted quickly to score from the rebound.
Del Rio equalised for Bristol 10 minutes later, breaking clear to round goalkeeper Marie Hourihan.
Blues then missed a penalty after Jemma Rose was judged to have pushed Jodie Taylor, who then saw her spot kick saved by Siobhan Chamberlain.
Moments later, Williams hit the bar with a header following another corner but it was the Vixens who took the lead early in the second period when James drove a fierce 30-yarder high into the net.
But Jade Moore headed home from Jo Potter’s cross to ensure Blues didn’t succumb to their first defeat against the Stoke Gifford Stadium outfit.
Hourihan made a good save with her legs to prevent Del Rio re-establishing Bristol’s lead, and Potter almost grabbed all three points for Blues in stoppage time from a free-kick.
Bristol Academy: Siobhan Chamberlain, Loren Dykes, Jemma Rose, Grace McCatty, Corinne Yorston, Natasha Harding, Angharad James, Michelle Green (Ellen Curson 71), Alexandra Windell (Ann-Marie Heatherson 90), Nicola Watts, Laura Del Rio.
Subs not used: Rhian Cleverly, Ellie Leek.
Goals: Del Rio (12), James (49)
Bookings: McCatty (74)
Blues: Marie Hourihan, Chelsea Weston, Laura Bassett, Emily Westwood, Kerys Harrop, Karen Carney, Jo Potter, Jade Moore, Rachel Williams, Eni Aluko, Jodie Taylor.
Subs not used: Emily Simpkins, Izzy Christiansen, Hannah George, Rachel Unitt, Maz Ballard, Crisy Torkilden, Rebecca Spencer.
Goals: Williams (2), Moore (51)
Bookings: Weston (65)
Referee: R. Cox