The Town boss twice saw his side come from behind at Highbury to keep alive their play-off hopes.
"I think we've earned the three points but we shot ourselves in the foot within three minutes after going behind so early," said Alexander.
"We put ourselves in a poor position and the fight back from the team was great - to come back into it not once, but twice. It's very rare at this level teams go behind and get points.
"We needed to be more aggressive defensively and in the second half the players involved responded to the message. If you have that right commitment and mentality you can keep a team like Gillingham at bay.
"The lads are disappointed they haven't won this - that's good to see that they are disappointed with just a point."
Gillingham looked in for an easy ride when they took the lead after just three minutes. Nathan Pond gifted the ball to Callum Davies who set up Danny Kedwell to apply an expert finish for his 14th goal of the campaign.
But Fleetwood refused to roll over and equalised just after the half-hour mark. Junior Brown's cross was headed against the crossbar by Gareth Evans but record signing Jamille Matt was perfectly placed to nod home the follow up.
The visitors regained the lead before the break, Charlie Allen with a free header past Scott Davies in the home goal.
Alexander's team were far from buried and pulled level again with just over 20 minutes remaining. Brown forced his way through a crowded area and Matt got the final touch.