"We let in two soft tries and that puts too much of a gap between us," he said.
.."I thought they won most of the physical battles, but that's life. That's the pressure of the big day when fatigue kicks in. We had our chances, but we didn't execute them well enough. You've just got to cop it sweet.
"The club, the players and our captain Martin Corry have done an amazing job this season. I'm immensely proud of all the guys.
"We simply fell short today. We weren't good enough and full credit to Wasps."
Howard said the final was proof that England would be a force at this year's World Cup.
"English rugby is in great shape," he said. "You've got good teams and good players here."
Corry added: "The two tries cost us the game. All credit to Wasps - we thought we'd marked everything at the lineout, but they found holes.
"In the second half, we gave it everything, but you can't gift a side like Wasps 10 points.
"Looking into the lads' eyes after the game, I know they gave everything out there."