Wolves looked set to be denied the win they needed to go top when Billy Clarke popped up with an injury-time equaliser to cancel out Bjorn Sigurdarson's seventh-minute strike.
Crawley more than deserved a point but Leigh Griffiths denied them with a penalty in the fourth minute of stoppage time - much to the relief of Jackett.
"We can play better," said Jackett. "We have an improvement in us and more gears to come.
"Being 1-0 up for that length of time you know that the opposition are going to attack you and what we should have done was finish our chances off on the counter attack as we
had numerous chances when we could have put the game away.
"You could see the equaliser coming because of the quality of Crawley's play. But we did fantastically well to dig out a win in injury time.
"I am delighted with the win but there is an improvement in us. But we have just won three games on the trot and winning three consecutive matches at any standard of football is good.
"Our aim is to win promotion and nobody gets promoted in August. There is a long way to go and a lot of hurdles we have to overcome but we have 10 points from 12 and that is
a good return."
Jackett insisted that there was no doubt it was a penalty when Kyle McFadzean handled Kevin McDonald's cross.
He added: "I have seen it again and in this day and age when the hand is away from the body then I think it is a penalty. My opinion is it was the right decision."
Crawley manager Richie Barker revealed that his players were devastated by the defeat but feels that there were more positives than negatives for his side.
He said: "What was pleasing was the amount of chances we created and it was an excellent finish from Billy.
"But in terms of the way we played, hopefully we will have gained some friends tonight throughout the nation, who have been watching, and hopefully we will get the respect that I think we deserve for the way that we play.
"It is very tough to take but we have 42 games left and if we play like that in most of them we will win more than we lose.
"We were certainly the better team in the majority of the second-half. I thought we paid them too much respect in the first 15 minutes of the game. It was a bit like rabbits in the headlights. But to be fair to them they weathered the storm and I thought we were excellent.
"The thing is here that you can quite easily go under with the noise that the crowd make, but we got back into it."
Barker had a different view of the penalty to that of Jackett as he felt that McFadzean was unfortunate to be punished.
He added: "I think the ball has been pulled back behind Kyle and the momentum means it hit him on the arm.
"Apparently the referee (Simon Hooper) said to the lads that he didn't think it was but that linesman thought it was."