Right winger Ben Jones-Bishop scored two first-half tries as Leeds led 10-6 at the break but they were only able to breathe easily when left winger Ryan Hall touched down five minutes from the end. A first defeat in five matches dents the Wildcats' play-off hopes but they will get the chance to turn the tables at the Rapid Solicitors Stadium next Friday.
"I thought we had the momentum in the last 20 minutes and that we were going to come home strong but we came up with some more errors," Agar said.
"I'm pleased with our defensive efforts. I thought they were outstanding but we asked too much of ourselves defensively and we got caught out by a couple of kick plays.
"We had a lot of defending to do but I thought our attitude in that area was superb. We just didn't have enough good ball to win the game. I don't think our performance with the ball was great but the desire is there for all to see. We're looking forward to next week."
Wakefield lost prop Andy Raleigh with a suspected fractured cheekbone which is set to rule him out for the rest of the season and will also anxiously await news of the knee injury sustained by skipper Danny Kirmond.
Leeds, too, suffered a major injury blow, with England centre Kallum Watkins going off with a twisted ankle after 65 minutes but coach Brian McDermott hopes to have skipper Kevin Sinfield back for the trip to Wakefield.
The champions sorely missed the calming influence of the captain as they failed to make the most of a lion's share of possession but McDermott preferred to praise Wakefield's defence.
"I've got to give Wakefield credit," McDermott said.
"I'm sure it was very frustrating what we did offensively and I'll concede we should have scored an extra try. But Wakefield are a threat, they can attack, and I thought defensively we were outstanding."