Rovers, who went into the game minus several first-team players, looked to be heading for a well-deserved point after Eliot Richards cancelled out Danny Coles' opener.
However, the Grecians secured the points thanks to debutant Sam Parkin's winner 11 minutes from time.
"It's not ideal with all the injuries we have," Ward said. "It is what it is and I can't alter that. I can't make injured players fit, so we have to go with what we have and try our very best.
"We tried our very best with the ones we got and people will have varying views as to whether it was the right result or not. I think we could have got a point out of it, but I don't think we could have tried any harder.
"We took too long to get going, but that isn't a surprise with it being the first game of the season. We got at them in the second half and could have snatched a draw at the end.
"Had we scored in that melee, then everyone would have said what a dogged performance it was, so it shows you how fine these margins are in football."
- Sports & Recreation
- Danny Coles
- Eliot Richards