Stormers head coach Allister lamented his team's slow start in their fifth round 36-20 Super Rugby loss to the current champion Chiefs in Hamilton.
The Chiefs led by 17-6 at half-time, and by 24-6 three minutes into the second half, before the Stormers launched a fightback to make it 24-20 going into the final minutes of play.
Unfortunately for the 2011 and 2012 SA Conference champions they were not able to sustain the pressure and two late Chiefs tries saw them miss out on a losing bonus point too.
"It's another disappointing loss for us," the coach admitted on the Stormers site.
"We started off badly, but credit to the Chiefs. They attacked us (out) wide and we felt the pressure there and came out of our line a few times, which proved to be costly. Last week the Crusaders attacked us from close-range, but the Chiefs found the necessary space out wide in this game."
The Chiefs scored two tries in the first half and three in the second half, two of those second-half efforts coming in the last four minutes of the game.
"They're not the double defending champions for nothing, you know," added Coetzee.
"We had a much better second half and we came back nicely into the game. There was a belief in the team at that stage but the Chiefs closed the game off well and punished us at the end (for our mistakes)."
The Stormers will now ravel to Sydney where they will be based in the lead-up to next weekend's game against the Brumbies in Canberra. They will then finish their tough four-match tour with a final fixture against the Reds in Brisbane the following Saturday.
"We're beaten, but unbowed. We've had a tough tour of New Zealand against two quality teams - the Crusaders and the Chiefs," said Coetzee.
"We will now close the chapter on the New Zealand leg of our tour and are looking ahead to our (two) remaining games in Australia.
"The one big positive is that we have eight days until our next game (against the Brumbies), so we will lick our wounds and get up for that game," added the Stormers boss.
Lock De Kock Steenkamp (groin) is a major injury-worry for Coetzee after the Chiefs game, whilst Ruan Botha (knee), Jean de Villiers (knock to shoulder) and Jaco Taute (AC Joint) were also nursing injuries.
"De Kock is definitely the biggest concern for us at this stage," added Coetzee.
"Jaco felt his shoulder a bit and went off, Jean took a small knock and Ruan complained about his knee after the game.
"We have a travel day on Saturday, we are flying to Australia (Sydney), and once we are there will be able to properly assess our injuries after they go for scans."
Lock Rynhardt Elstadt, hooker Scarra Ntubeni and prop Pat Cilliers have all flown home from the tour because of injuries thus far, joining high-profile players Eben Etzebeth, Manuel Carizza, Juan de Jongh and Cheslin Kolbe on the sidelines with long-term injuries.