Parkinson's men put in two very encouraging displays last week against Preston North End and Wolverhampton Wanderers - both teams tipped for the top this season - but came away with only a single point to show from the two games.
Looking back at both matches individually, there can be no doubt that City more than held their own in two of the more challenging fixtures they are likely to face this League 1 campaign.
Pleased as he might be by his side's showings against Preston and Wolves though, Parkinson wants his players to kick on and ensure they get their rewards in matches.
Parkinson said: "We have been playing well. Against Preston and Wolves in particular, that was two good performances from us against two good sides.
"But we only have one point (from the two games).
"We have to use the confidence gained from those performances against two of the better teams in the league to help push us on.
"We also, however, have to make sure we don't pat ourselves on the back too much. We can't sit here and say 'fantastic, well done' because we have only got one point from those two games.
"We have to take the confidence from the Preston and Wolves games into the Crewe game but also have that little bit extra determination about us as well.
"We have to reproduce our good recent displays but make sure that a good display is turned into three points."
Hosts Crewe go into Saturday's game in the relegation zone after their 3-1 defeat at the hands of Nigel Clough's Sheffield United last weekend.
Following a run of only two league wins from their last twelve games, Crewe boss Steve Davis has hinted that he could be looking into making changes for the visit of Parkinson's side.
Davis has already brought in 18 year-old midfielder George Evans on loan from Manchester City and more could follow him through the Alexandra Stadium entrance before Saturday.
Regardless of Crewe's eventual line up come kick off though, Parkinson says City will be best suited concentrating on their own strengths.
Parkinson added: "Crewe have brought a loan player in this week (Evans) and could bring one or two more in before this Saturday.
"They have been changing their personnel and set-up about a little bit, so we can't try to second guess them too much. We can only focus on what we can do in the game.
"We have to make sure we bring our a-game to table and approach the match in the right manner. If we do that, I think we'll be a difficult team to contend with."
Despite coming off at half-time during last Saturday's home encounter with Wolves due to a tight hamstring, Raffaele De Vita should be fit enough to be in contention for the weekend after Parkinson confirmed the substitution was only a precautionary one.
With Nahki Wells also pushing for a starting spot following his recent spell out with an ankle injury and Andrew Davies (knee) currently the only sidelined player, Parkinson acknowledges he has some selection decisions to make ahead of the trip to Crewe.
Speaking about De Vita and his slight hamstring problem from last week, Parkinson said: "I don't think Matty Barrass (Head Physio) was overly-concerned about it and we probably just caught it at the right time.
"If he had of gone out there (for the second half), he probably would have damaged it to a greater extent.
"There was no need to take that risk with Raf, especially considering he was in the middle of his second game in four days after not having too much football before that previously.
"There was some definite fatigue there, so we took the decision to take him off and I believe we will reap the benefits this week."
Parkinson continued: "Apart from Andrew (Davies), everyone is ready for action. Training has been good this week. It has given us the chance to rest a few with bumps and bruises.
"I didn't mind it when a few of the lads missed out on training early in the week because, after three games in seven days last week, I felt the likes of Gary Jones needed a little bit of a well-earned breather in the gym.
"Everyone has trained well today (Thursday), however, and it gives us some thinking to do before we name the team either tomorrow (Friday) or Saturday in the dressing room."