A debut goal from recent loan signing Jamie Proctor midway through the second period cancelled out a second-minute opener from Vale striker Ajay Leitch-Smith to see City earn a share of the spoils at Vale Park.
Parkinson's men had to play for virtually an entire half with only ten men following Evans' red card for a lunging challenge on Valiants midfielder Anthony Grant just minutes after the restart.
Reviewing the game, Parkinson: "We started slowly, and that annoyed me.
"We do our homework on the opposition - I drove all the way down to London last Sunday for their (Port Vale's) match at Millwall - and we knew Leitch-Smith's runs in behind can cause problems.
"We showed the lads examples of these runs yesterday (Friday) but we didn't switch on from the start and we got punished for it.
"After the disappointment of Tuesday (losing in the FA Cup), to concede early on in this game was clearly a blow but I thought we were magnificent in that second period.
"Even with ten men, we have contained Port Vale, restricted them to long range efforts and got the goal ourselves.
"We know ourselves that it can be hard to play against ten men, and we put into practice everything that we have seen other teams do against us in recent matches.
"After equalising, we've had one or two moments to maybe go on and get something more. I was very pleased with the lads' efforts."
A day after putting pen to paper on a one-month loan deal from Fleetwood Town, Proctor netted his first City goal in front of the away fans when he powered home a header from half-time sub Mark Marshall's cross.
Parkinson added: "With Mark, he has produced for us this (Saturday) afternoon.
"I said to the boys before the game that we have to put pressure on ourselves to produce, to show that quality in the final third.
"Marshy has produced a fantastic cross and it is a striker's dream really.
"Jamie led the line well, won a lot of things well in the air and linked up well with (Billy) Clarkey.
"To cap it off, he has scored a really good centre forward's goal."