Graeme Murty said Ranges are struggling to find confidence
The Dark Blues celebrated their first home win over the Ibrox side in 25 years thanks to goals from Mark O’Hara and Kevin Holt, with Joe Garner grabbing a consolation.
The result saw Rangers – who are without a manager following Mark Warburton’s departure 10 days ago – fall six points behind second-placed Aberdeen as their season goes from bad to worse.
Murty said: “You saw a team that struggled to turn it around when things went against them.
“When your confidence takes a knock that can be a symptom. It’s disappointing. It’s not easy to put into words the emotions I and the players went through. We have to be better than that and it’s not acceptable. We know that and they know that and we’ll take this on the chin.
“But there are more than enough characters in the squad to turn it around.”
Rangers fell to a 2-1 defeat at Dundee
Jubilant Dundee manager Paul Hartley felt the margin of victory could have been greater.
He said: “I never thought we were in danger today, even when Rangers scored, because that came from the one time we didn’t press properly. We were never in trouble.
“It could have been more. We had good opportunities to score more goals. But to get a win against Rangers, the first time since 1992 here, it has been a long time coming. The fans will be happy with the win and the way we played, the performance.
Hartley urged his players to maintain this standard for the remainder of the campaign after the result lifted them up to sixth place in the Premiership table and eased their relegation worries.
He added: “The challenge for us is that it can’t be one-off because it’s Rangers.
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“We have to be like that every day.It takes us into the top six but it’s about the manner of the win. We know we’ve got that in us. Consistency has been our problem.”
O’Hara made it two goals in two games against Rangers at Dens Park this season.
The midfielder sent his side on their way yesterday with the 13th-minute opener and he lay the gauntlet down to his team-mates to secure a top-half finish.
O’Hara said: “It is a massive result for us and I don’t think a lot of people would have had us down for it. We were all hungry and fighting for each other. If we want to stay in the top six it is something we will need to keep doing.”
Rangers defender Clint Hill was taken off complaining of blurred vision after a clash of heads and will be assessed by medics.