In their first appearance in the top flight since 1962, the Bluebirds were undone by goals from Hammers midfieldersJoe Cole and Kevin Nolan.
"We started slowly but after that we had an awful lot of possession. We knew we were coming to a good team in a good atmosphere," Mackay said.
"They were clinical with Cole's goal and while we had plenty of possession, there was no penetration. We grew into the game in the second half.
"Overall I can't be too harsh on my players because we gave a good account of ourselves. We weren't overawed and that showed."
Mackay revealed new signing Andreas Cornelius will return to training next week after missing the match with an ankle problem and announced that additional recruits could be heading for Cardiff City Stadium.
"We're trying to get new players and we'll keep trying to do that, but sometimes it's not always in your control," he said.
"If I find a good player and everything comes together in terms of the club and player agreeing everything, I'll absolutely try and act."