Owls playmaker Forestieri was introduced at the interval and gave Wednesday some much-needed impetus.
Tom Lees headed home the game's only goal to seal a first win in seven for the hosts - at the same time extending Bolton's wretched run to just one win in 15.
"I thought Sheffield Wednesday were there for the taking tonight," said Parkinson.
"Our goalkeeper has hardly touched the ball or had a save to make.
Police incident Woodhouse Sheffield: Two men and a woman injured after large fight breaks out on Market Square
Sheffield fire: Crews tackle blaze in Wharncliffe Woods near Oughtibridge as heatwave continues
Sheffield fire: Video shows firefighters battling blaze at Wharncliffe Woods near Oughtibridge
Sheffield Crown Court: Here are the biggest cases from the last week including paedophile sting
Sheffield weather: Heavy rain set to lash city as Met Office extends thunderstorm warnings until Tuesday
"I thought Fernando Forestieri coming on for them gave them a big lift.
"That start to the second half has cost us the game tonight.
"One moment has separated the two teams."