The visitors were seconds away from nicking a win at the Gallagher Stadium but conceded an equaliser in stoppage-time.
Doswell admitted a win would have been a bit of a steal and was happy to take a point.
He was also delighted to see his side stretch their unbeaten start to 10 games and consolidate second place in the table.
‘It was a brilliant game of football and to be honest we were lucky to come away with a point,’ said Doswell.
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‘Maidstone put us under a lot of pressure and Ross Worner pulled off six or seven fantastic saves.
‘It would have been a massive nick if we had held on.
‘Maidstone certainly deserved to get something out of the game.
‘They were dangerous and had more energy than us which wasn’t surprising.
‘Playing on Wednesday didn’t give us a lot of recovery time.
‘All credit to my players, though, because it was a brilliant away point considering how many were out there playing with niggles and injuries. It was a fantastic team performance and at the end I was just hoping we might get away with it.’
The Hawks started well enough but it wasn’t long before the Stones got on top.
Worner produced a couple of good saves before the hosts took a 26th-minute lead.
Jonathan Edwards pounced on a poor back-header from Sam Magri and lobbed the ball over Worner.
The Hawks were gifted a way back into the game midway through the second half when Roarie Deacon was clumsily brought down inside the area.
Anthony Straker sent Maidstone keeper Jake Cole the wrong way to level the scores.
With eight minutes of the game left, substitute Danny Kedwell made a dramatic entrance.
Sent on before a corner he scored with his first touch – heading in at the far post from the set-piece
‘It was a great header and I’m so pleased for him,’ added Doswell.
‘He isn’t really fit enough to even be on the bench.’
Two minutes into stoppage-time, just when it looked as though the Hawks would hang on, Dan Wishart headed in a cross at the back post.