Parkinson's men drew their final encounter of 2013 this Sunday after goals from Rory McArdle and Swindon's Alex Pritchard to leave City in the top half of the Sky Bet League 1 table going into the New Year.
McArdle, who returned to the side after missing the Rotherham United match on Boxing Day due to suspension, powered City into the lead with a thumping first half header from a Gary Jones corner.
A fine individual goal from Pritchard - on loan to Swindon from Premiership giant Tottenham Hotspur - levelled things up for the visitors in the second half, however, to ensure both sides picked up a share of the spoils.
Parkinson said: "Swindon play that extra man in midfield and make it tough for you.
"When you have two games coming quickly as you do at this time of year, that extra man in midfield from the opposition can make getting possession tough at times.
"I felt we coped with that well, however, certainly in the first half.
"We got the lead, which is something we'd been craving because we hadn't had that at home for a while, but unfortunately for us (Alex) Pritchard has produced a tremendous goal.
"We look at the boys and their defending, as always, you think you can do better but it definitely was a top-class goal.
"We have conceded a few goals out of the top draw recently. I think that is the division we're in though - there is certainly that extra bit of quality around. Look at the today (Sunday) and Boxing Day, we're conceded great goals on both occasions to players on loan from Premier League sides.
"We showed great character and kept going after their equaliser though.
"Ollie McBurnie has come on and put a great ball into the box, (James) Hanson's had a good chance with a header, and (Kyel) Reidy's worked his socks off down that left-hand side.
"We couldn't quite get the winner but, after getting beat on Boxing Day, we'll take a point."
City's festive match-up with Swindon marked the halfway point of their Sky Bet League 1 season, meaning the Bantams have now gone up against every other team in their division at least once.
With Parkinson's side currently sitting tenth in the league after twenty-three games and the January transfer window just around the corner, the City chief says he know what the club need to kick on in the second half of the season.
Parkinson said: "We've just got to look for that little bit of extra quality to kill teams off.
"The spirit and commitment of the squad is without question - they were on their last legs in the dressing room after the game. They have given us everything again today.
"But we have to look to improve.
"We have a big game at Notts County on New Year's Day and then we have to sit down, myself and the chairmen, and see how we can move things round to get that extra bit we need.
"We've had a terrific year - no-one could have predicted back in January that we'd get promoted, get into two Wembley cup finals and find ourselves tenth in League 1.
"My message to the supporters now, however, is that I'm looking to get better, and we have to do that. I'll be trying everything I can to move things around. If there isn't the money there to spend, I'll have to create it within the squad.
"We need to make sure we give the core of this team a lift by giving ourselves a little bit extra.
"Our last two goals conceded have been outstanding efforts from players on loan from Premiership clubs. That is something we have to look at - getting that extra bit of quality to add to what we have in the squad already.
"The spirit and effort of the lads is undoubted but, when we get into that final third, we need to produce. If you look at the recent run we've been on, we haven't played bad. We've played with determination and commitment but we've just lacked that final ball to win us games of football.
"The dividing lines can be that tight - it is something we need to probably sit down and address."