The clash at McDiarmid Park was seen as an opportunity for the Scottish champions to move a step closer to retaining the Clydesdale Bank Premier League title by increasing their lead at the summit to 13 points. Instead, they were handed what skipper David Weir branded a "wake-up call" afterwards and Whittaker concedes that complacency played a part.
"It probably did on Tuesday night," said the Ibrox full-back. "We need to put that right and we can't allow that to come into our game. We need to play at a higher tempo and it's important we do that this weekend. We were all disappointed on the night and it was definitely a wake-up call that there is still a job to be done so hopefully we can go on and win the next two home games.
"We all know we weren't good enough on the night. The manager spoke to us after the game and at training and we are all looking forward to the game against Hamilton tomorrow. The good thing about football is there is another game in a few days' time to put it right and that's what we will be looking to do."
Asked what manager Walter Smith had to say to his players in the aftermath of the defeat, Whittaker said: "Just that we can't take our foot off the pedal. There are still games to be won for us to win the title. Although we do have the gap, we can't rely on that. We need to do the job as quickly as possible."
Hamilton manager Billy Reid has challenged his players to showcase their recent form on the highest stage when they face the Ibrox side today. Accies have gone six matches undefeated in the SPL to achieve their best top-flight record for 70 years. The run has taken Hamilton 11 points away from bottom club Falkirk but Reid has been even more satisfied by the manner of the performances.
Kilmarnock manager Jimmy Calderwood praised Hamilton's attacking football in their recent 2-1 victory at Rugby Park, a scoreline that flattered the hosts.
"We all get caught up in winning games at times," Reid said. "Sometimes you win 1-0 and lose 2-1 and there is no difference in the performances. Some of our performances in the last few weeks have been exceptional. We have played some good attacking stuff and got the ball down. That's exactly what we're trying to achieve at Hamilton Accies. In the last five or six weeks we have been playing the way we want to. We are on the best run the club has had since 1939 and that's all credit to the players. This will be a good test to see how far they have come."
Hamilton have pushed Rangers close in recent games, with their Scottish Cup fourth-round contest only decided in extra-time of the replay at Ibrox. Reid will continue to encourage his players to show their footballing ability when they visit Govan today. "You need people to take responsibility and take the ball and stand up and be counted," Reid said. "If you make a mistake you will get punished so you have to be brave enough to take the ball. What I will say is it's a lot more difficult to beat them at their own place."