A Martyn Waghorn hat-trick and a fine goal from James Tavernier got Rangers back to winning ways as they defeated Morton 4-0 at Cappielow.
The result stretched the Ibrox side's lead to nine points at the top of the Championship.
"As a team we deserved a little bit more respect than that," he said.
"The boys were hungry, they felt disappointed after Tuesday. No-one wants to lose a game of football but also some of the comments were disrespectful to how they played for the first 11 games. They played 11, won 11.
"It speaks volumes for their character and their work ethic to then see the type of comments that they got hurt them, annoyed them, so they were waiting for today's game."
Despite the Cup exit Rangers still have a 100% winning record in the league, and after an early Waghorn penalty the result never looked in doubt with three goals before half-time.
"It was a good performance, but we have to look at it and say we can be more clinical," Warburton told BBC Scotland.
"We were a bit loose defensively at times, but we learn from it again hopefully.
"For the first 25 minutes we were excellent. We set the tempo, moved the ball well, got a couple of goals and we were in good shape.
"It's about them working hard to be better, and if we can do that we can be a good team."
Morton manager Jim Duffy was happy at the way his side responded to the goals conceded, with Alex Samuel and Denny Johnstone both going close to getting on the score sheet.
Duffy said: "We gave Rangers an invitation to control the game with the penalty. Once they got that opening goal they put us to task, their movement was terrific, we just had to try hang on as best we could.
"You don't want to capitulate and let the heads go down. Credit to the players, they never let that happen, it hasn't happened since I've been here.
"We were beaten by a far better team today, there's no disgrace in that. What would have been a disgrace is if we had thrown the towel in.
"The commitment was there but Rangers had the quality and that was the difference."
Rangers manager Mark Warburton said he felt his team had been disrespected in the wake of their midweek League Cup defeat to St Johnstone.