At this point, Liu Biao doesn't even have the capability to focus on recapturing Jingzhou. Internally, there's dissatisfaction from the Cai Family due to the several reductions of the navy because of a lack of funds, and externally, the Wu Creek Barbarians sporadically raiding, leaving him without the means to even counterattack.
To borrow a phrase, "You can't make bricks without straw" or "Poverty brings grief to the married couple"—essentially, without funds, Liu Biao and Cao Cao, despite having extraordinary talents in their ranks, are unable to utilize them fully.
In such a situation, Liu Biao could only pretend he saw nothing when he received Cao Cao's proclamation. Offending Cao Cao, the only person he could arguably call an ally, was not something Liu Biao would foolishly entertain.