George Thomas’ 39th-minute strike earned Mark Robins’ Sky Blues a fourth win in five home matches, condemning the Saddlers to a ninth away reverse of the campaign.
Eoghan O’Connell, who went closest for the Saddlers with a second-half header which was cleared off the line, was also sent off for two bookable offences on a disappointing afternoon.
“The first 45 was way below par," said Whitney. "It had an end of season feel to it and we have done everything we could to prevent that.
“You can’t be that below the standards you set, with the energy levels, and expect to get something from the game.
“I’d like to apologise to the travelling fans today. That first half was not acceptable.
“Second half we gave it a go but you can’t keep giving teams that first goal. We tried second half, we huffed and puffed, but we didn’t really create any clear chances.
“But the first-half performance was very disappointing, very lacklustre and I’ve told the players that.”
Whitney brought on Erhun Oztumer and George Dobson at half-time in an attempt to spark his side into life.
“Sometimes you’ve got do that,” he added. “We needed something because as a group they weren’t doing it.
“You have to make changes and I thought both of them did well when they came on. We started the second half much better but we didn’t get that equaliser.
“But the first half, I’m hurting. People say you’ve got nothing to play for but it’s still another defeat on the record.
“The fans want to see players who will run round and give everything they can. What you can’t accept is that first-half performance.
“There have to be people being accountable for that first-half performance because it was unacceptable.”