Bullard has impressed since returning from a long-term knee injury.
“You can’t keep a good man down, you can’t knock a guy like Jimmy,” said the Hull boss.
“Jimmy has got team-mates around him that are trusting him with the ball.
“That trust has brought a belief and that has brought confidence. Consequently we played some very good football.”
The Hammers had a 2-0 lead after 11 minutes, but Hull managed to bounce back and had the lead by the break.
“We found ourselves 2-0 down but we were playing well enough,” he said.
“We needed a bit of luck to get the first goal but then West Ham went on the back foot.
“Consequently we got a second and then a soft penalty – but a penalty nonetheless.”
