On a difficult Bloomfield Road surface, City put in a gritty display away at relegation-troubled Blackpool on Saturday to grind out a deserved victory over Neil McDonald's Tangerines.
Fresh from the Blackpool victory, Parkinson's men will now welcome another side at the wrong end of the division - Colchester - to Valley Parade this Tuesday evening.
Colchester currently occupy bottom position in the League 1 table but Parkinson says past experiences have told him that City will need to give it their absolute all once again if they want to pick up another win.
Looking ahead to Tuesday's night game Parkinson, who managed Colchester between 2003 and 2006, said: "We will need to show the same sort of resiliency and determination that we showed at Blackpool on Saturday.
"We want the lads to produce the same sort of performance as they did on Saturday.
"Saturday's game was a hard-fought one, as we knew it would be, and Tuesday will be no different.
"Blackpool were fighting for every ball and we know Colchester will come to us and do exactly the same. They will still believe they can get themselves out of trouble.
"Colchester signed two new players on Friday and they will be looking to improve.
"You only have to look at some of the scores in this division lately to see that teams at the bottom are improving and capable of picking up good results.
"We remember how hard we had to work for our victories at home to Oldham and Fleetwood recently - both sides who were near the bottom of the table at the time.
"To get the points on Tuesday, we know we will have to be at our best.
"Rochdale came to us in our last home game and rolled their sleeves up. They caught us cold a little bit and we can't let that happen again.
"It is all about our approach and the approach of the supporters.
"Our supporters are experienced enough to know that we might have to be patient at times.
"Colchester are going to look to make it difficult for us but we are looking forward to the game after Saturday's win."