Coventry were heading for a 3-2 win when defender Jordan Clarke handled as he challenged striker James Hanson just inside the visitors' box, referee Kevin Friend pointed to the spot and up stepped Nahki Wells to score to complete his hat-trick in the fourth minute of stoppage time.
Pressley said: "I thought we had dealt with everything that Bradford threw at us. I was delighted with the effort and a lot of aspects of our play. I am just disappointed we didn't get the result our performance merited.
"Credit to Bradford for pressurising us late in the game, but it was never going to be easy for us playing against long ball football. That is football from the dark ages, but we have got to learn to cope with it."
Bradford, who are without a win in seven league and cup matches, found themselves two goals down in seven minutes, but hit back through Wells to level the scores after 28 minutes only for Coventry to go 3-2 up in the 42nd minute.
Andy Webster scored the first in the second minute following a free-kick from skipper Carl Baker. Keeper Jon McLaughlin tried to catch the ball, but he appeared to be impeded by team-mate Rory McArdle and the ball ran loose to Webster to fire the ball into the net.
Before Bradford recovered, Callum Wilson took the ball off McArdle after chasing down a long pass from Blair Adams and, although McLaughlin knocked the ball away from him, it ran loose to fellow striker Leon Clarke to fire into the unguarded net for his 12th goal of the season.
Hanson saw his far-post header stopped on the line by keeper Joe Murphy before Wells pulled a goal back after 18 minutes when Hanson headed a long clearance from Kyel Reid over Murphy's head and into the path of Wells.
Hanson and Wells combined again for Bradford's equaliser, Hanson heading James Meredith's free-kick into the path of the Bermudian international to volley into the net.
However, Wilson restored Coventry's lead three minutes before half-time with a close range angled shot after getting the better of defender Matthew Bates.
Both sides had chances in the second half before Wells' last-gasp equaliser.