The Cod Army staged a second-half fightback to keep their top-three hopes alive. A Jamie Cureton goal handed the hosts the half-time lead but Antoni Sarcevic levelled from the penalty spot shortly after the break before Josh Morris drilled home the winner.
The result leaves Fleetwood three points behind both third-placed Rochdale and second-placed Chesterfield, with League Two leaders Scunthorpe a further two points in front.
Alexander said: "There are three games to go for all of us but we can only control our own points total.
"We have to go for maximum points from every game - if we do that we give ourselves a good chance. We can't control the other results, we just have to control our own.
"I naturally believe there is more pressure on the teams above us. It is human nature that if you have something you want to hang on to it and sometimes you make the wrong decisions.
"I said 10 days ago that I didn't think the top three were secure."
On the game against Cheltenham, Alexander added: "We got ourselves on the back foot with the first-half showing and conceding the goal and we had to dig deep to get three points. The players did that and it was great to see because the second half was much improved.
"It is all about players - players win games - and they showed the right spirit. It had to be more spirit and more tempo because we know the quality is there.
"We played really well in the second half, we had to defend at times but when we had to we stood up to it.
"The response from the players was great and they deserved the win. They have to realise that their destiny is in their own hands."