Nahki Wells took his tally to 21 for the season with a brace. Andrew Davies and Garry Thompson were also on the scoresheet for Bradford, while Tom Hitchcock grabbed a consolation for the Pirates.
The result ended Rovers' unbeaten run of five matches and Ward said: "Bradford were on the front foot from the outset and were very positive with their football.
"We made errors by giving the ball away and we got punished for them. Four individual mistakes led to Bradford's goals and when that happens you know it isn't going to be your night.
"I have no excuses for the players. The lads have got to learn from this quickly and improve.
"Bradford are very strong and were a better side than us on the night and they are going to take some stopping if they can continue that form.
"We've got to remember that three or four months ago we were staring down the barrel of relegation. We've been good enough to get ourselves out of trouble, but we have a lot of work to do to be as strong as Bradford."