The Croat, who lost in four sets, accused officials of favouring the home player and said he felt "cheated".
Wimbledon 2012: Andy Murray - winning is all that matters
"It was outrageous, outrageous," he said. "It's Wimbledon, Centre Court, and they do this. The whole credibility of this tournament went down for me."
Murray responded: "That's very tough to question the integrity of Wimbledon."
He added: "It's got a lot of history, a lot of tradition. There's been hundreds of thousands of matches played here over the years. I've never heard that before.
"But I need to see the videos. If there was 11 foot faults called against him and every one was incorrect, then that's completely wrong and unfair.
"But for it to happen that many times, you would think there would have been a number of fairly obvious foot faults, because you don't really see them called that much nowadays."
Tim HenmanFormer British number one and BBC Sport commentator
"In the Davis Cup, you always feel like a few calls go against you. With a foot fault, you are implying that the line judge is cheating, because you can't judge for yourself as you're focusing on the ball. It's something he will regret saying in the morning. You can't question the integrity of this tournament."
The momentum swung both ways early in the match, but Karlovic was left frustrated when Murray successfully challenged what appeared to be a second-serve ace to win the first set.
The second set followed a similar pattern, with Karlovic holding his nerve to level the match up.
A pinpoint lob saw Murray break early in the next set and he repeated the feat in the seventh game on his way to taking a 2-1 lead.
It took a tie-break to separate the two players in the fourth set, with Karlovic's fate sealed when he served a double fault at 4-4.
Murray was made to work hard for his victory, but Karlovic claimed he could have won had it not been for the officials.
When asked what was the difference between the two players, he replied: "Foot faults. I don't know what to say, but it was a little bit outrageous.
"In my whole life, ever since I was eight years old, my whole life I didn't do this many foot faults. It was like 11.
"After I don't know how many, I stood a little bit back so they cannot call (foot fault). They still did it."
An All England Club spokesman responded to the accusations by saying: "If he wishes to make a formal complaint then all evidence will be reviewed."
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