Dale Benkenstein has played down hopes of pushing for victory at Durham.
Hampshire will begin the final day of their County Championship division one clash at Chester-le-Street 60 runs in front after the home side declared their first innings on 421 for nine.
But Benkenstein reckons thoughts of setting Durham a victory target are premature.
Hampshire’s first-team coach said: ‘We’re not yet thinking about setting a target.
‘Durham will be trying to win the game, so we have to bat well this morning and see how the first session goes.
‘The pitch has played better than we expected but to come up here and compete as we have has been a good effort.’
Keaton Jennings (129), Jack Burnham (74) and Ben Stokes (51) had Durham handily placed at 295 for three only to lose six wickets for 54 runs.
But Hampshire, who went into the game sitting rock-bottom of the top-flight table, were hampered in their attempts to bowl the hosts out after Ryan McLaren picked up a hamstring injury.
The paceman, who had already picked up three for 78, is likely to be sidelined for a couple of weeks.
And in his absence, Durham’s last-wicket pair put on an unbroken stand of 72 to frustrate their visitors.
Barry McCarthy struck a career-best 51 not out, while Graham Onions was unbeaten on 23 when skipper Mark Stoneman called time on the innings.
With McLaren off the pitch, Gareth Berg (two for 70) and Gareth Andrew (three for 104) both got through 30 overs.
Benkenstein praised their efforts but admitted the resistence from his former county’s tail-enders had probably cost Hampshire their hopes of a much-needed victory.
The Ageas Bowl chief added: ‘Ryan has a hamstring injury and could be out for a couple of weeks.
‘Once we were a bowler down, Gareth Andrew and Gareth Berg were outstanding.
‘But the last-wicket stand was a thorn in the side.’
Jimmy Adams and Will Smith negotiated the final six overs of the third day’s play and will both resume on four not out this morning.
– ROB ATKINS