Alan Archibald's side are eighth in the SPFL Premiership standings heading into the international break but could have found themselves far higher up the standings if they had been able to turn their dominance in games into points.
A lack of cutting edge in the final third has cost the Jags dear so far this season, with Dundee United, Hearts, Kilmarnock and Hibernian all leaving Firhill with points to their name.
Thistle were again profligate in front of goal on Monday night as Liam Craig snatched victory for Pat Fenlon's side and Higginbotham knows the Jags must start hitting the goal trail.
He said: "It was the same old story for us. Aberdeen are the only team to give us a doing and we can't keep having the hard luck story.
"We have to take our chances when they come along. We should have a lot more points on the board and the gaffer has said that.
"We know how well we can play and we have shown that this season. We need to pick ourselves up and kick on and hopefully we can get a win at Inverness next weekend.
"It is really frustrating. We are playing really good football and we created four or five really good chances on Monday night.
"If you don't take them, you don't win games in this league. The gaffer said that last year we would probably have got away with it but in the Premiership it only takes one chance for the opposition to do you.
"Teams are getting one chance against us and scoring while we are creating four, five, six chances every game and only taking one of them, We need to start finishing them."
Archibald's side will round off the first quarter of the season against the top two teams in the Premiership once the domestic calendar gets back up and running next weekend.
A trip to Inverness is first on the agenda for the Jags before champions and league leaders Celtic visit Firhill.
Thistle have adapted well to the rigours of top flight football this term and summer signing Higginbotham is confident they can look onwards and upwards after a solid start to the campaign.
He said: "We are going into games thinking that we can win them all.
"We have almost played every team in the league and Aberdeen are the only ones who have beaten us well.
"All the boys are confident that we can win games in this league and the boys have shown that we are capable of pushing up the league.
"Obviously, the aim is to survive but we want to be finishing in that top six.
"Last year, if we had been playing these teams in the cup people would probably have been thinking that we would get beat.
"Now we are coming away with draws and thinking that we should be winning games. It does show you how far the club has come."