The striker opened the scoring with his second goal of the season, giving the hosts an advantage at the break.
But an error-strewn spell just after the restart allowed Matthew Lund to level and claim a 1-1 draw for the visitors.
It is not the first time this season United have struggled to get going after an interval and Constable knows they need to find a solution quickly.
He said: “We need to look at how we start the second half and figure out what is going wrong to put it right before it costs us too many points.
“The second they scored, we came alive again, but it takes a goal to kick start us.
“If we can sort that out I’m sure we’ll have plenty to go on and beat teams.
“It has happened away but it seems to happen more at home – it’s almost like we take our foot off the gas.
“They are obviously a decent side but it gives them half a chance, which they took.
“It’s little things we need to work on to make sure we’re all on the same page and make sure we don’t concede.
“I think if we hadn’t conceded we would have won by three or four.”
While there were elements to work on, the 28-year-old remained upbeat.
He said: “There will be people who look at it as a missed opportunity. “The lads are trying to look at it as another point gained.
“They are a decent side and we knew they were going to make it difficult for us.”
Constable’s 24th-minute strike was a classic poacher’s finish, converting a rebound after Danny Rose’s shot was parried into his path.
It was his first goal since the birth of his daughter, Amelia, a week earlier.
She was in the crowd for the first time and Constable could not resist performing a baby rocking celebration.
He said: “Rosie did brilliantly to make the keeper pull off a save and it dropped nicely for me to tuck it in.
“I don’t like going too many games without a goal and it was nice to have the family here with the little one. “They all came so it was nice to get a goal.
“Hopefully she’s a lucky charm for me.”