Watford beat Hull City 2-1 away from home at the weekend and are now just three points behind the Tigers, who are sitting sixth in the Championship standings.
The Hornets made a slow start to the season but have won three of their last four league games to give themselves a bit of momentum.
Watford have been known for their managerial merry-go-around under their Italian owners over the several years, but Parkin feels the lack of chaos this season is something the fans are enjoying at the minute.
He also believes Ismael has impressed with his tactical flexibility when everyone expected him to turn Watford into a very direct team.
The former Championship star insisted that the Watford fans have bought into Ismael’s football and Watford have a decent chance of getting into the playoff spots this season.
Parkin said on the What The EFL Podcast: “I don’t know if it’s a slow burner but I just think the lack of chaos is being enjoyed by the Watford fans.
“Obviously, a manager that is showing different strings to his bow.
“We thought he was going to be very direct and uncompromising but they have been anything but like that.
“They are playing some nice stuff.
“They have got a striker that gives them a platform to play into and tactically they got it spot on at the weekend in terms of his changes.
“The supporters seem to have taken to Valerien Ismael and yes, it took a little bit of time but they are showing themselves to be a pretty cohesive unit.
“I’d say they have got a good chance of making it into sixth.”
Watford will host an in-form Southampton side at Vicarage Road next weekend in what could be a key test of their promotion aspirations.