Eighth-placed Boro find themselves seven points off fifth-placed Weston-super-Mare with just five games left this term after their loss to the in-form Somerset side Taunton on Non-League Day.
But with fixtures against Weston, sixth-placed Chesham and Yate Town - in seventh - all still to come in the final run-in, Gale says he will not be giving up hope until it is become mathematically impossible to secure a top-five finish.
And the Boro boss reckons if his troops replicate the high level of performance shown in their ‘cruel’ Taunton defeat then they will give themselves a good chance of a late-season surge to make the play-offs.
‘It's a bitter-pill to take but no-one is throwing the towel in. It's important we keep building on that (performance against Taunton),’ said Gale.
‘You know what, I'm proud of the players, it was an excellent crowd again. They were clapping us off and you know you've put in a decent performance
‘We didn't deserve to lose that game, they were lucky, really, I thought there were some key decisions in the game - Ellis has made some good saves (in the) second half. Their keeper has made some unbelievable save - the one that hits the post (from Bradley Tarbuck header) - he touches, he's made three or four decent saves.
‘I thought we should have had a penalty first-half. Billie Busari, they kicked him out of the game, he's got a massive gash down his leg from a tackle which, for me, was a red card.
‘We looked to play in a way and they couldn't live with us if I'm being honest, but they've come away with the three points. We felt with 10 minutes to go we had to go for it and their goal was cruel, really.
‘It's the frustration of a little bit of us, as a team you've got to take your chances, if we take them we go onto win the game.’
Billie Busari had an early penalty appeal waved away by referee Alex James while Luke Hallett and Busari himself had good chances to give the hosts the advantage.
Bradley Tarbuck saw a header early in the second-half expertly tipped onto the post by William Buse in the Taunton goal. Then, on 84 minutes, Boro were dealt a sucker-punch when Tobias Holmes was left unmarked to tap home from close range after Ellis Grant had earlier made two crucial saves.
Meanwhile, Gale explained the situation with forward Nick Dembele after he dual-signed with National League South Braintree.
Dembele came off the bench on 82 minutes for Boro against Taunton and Gale told how he'll assess things with the forward between now and the end of the season in terms of whether he turns out for Boro or higher-level sixth-tier outfit Braintree.
Gale said: ‘He (Nick) hasn't played a lot, he's come back from an injury and hasn't been able to force his way back in the team. He had a nasty ankle injury, to be fair, he did great for us at the start of the season.
‘They (Braintree) came onto me on Thursday and asked if they could do something with him. I spoke to their manager (Ryan Maxwell at Braintree) - I don't want to stand in the kids way - it's a higher level and I've allowed him to sign there. We'll see what happens come next week.’