The ongoing Ashes series has been marred by a number of controversies over the effectiveness and implementation of the Decision Review System (DRS), particularly the apparent failure of Hot Spot to detect when a player has edged the ball.
The ICC responded by flying Allardice in from Dubai for talks with players from both teams - but stressed the move was not prompted by a report from Australia's Channel 9 which suggested players were applying double layers of silicone tape to the outside edge of their bats to beat the thermal imaging camera.
And Allardice himself insisted that subject was not on the agenda.
"That certainly wasn't the purpose of the meetings," he told BBC Radio Five Live. "We were there to discuss DRS from a more holistic point of view.
"I think the reaction from both teams has been pretty consistent. Players have had stickers and reinforcement tape on their bats for years, it's perfectly legal under the laws of the game.
"I don't think there's any deliberate attempt to defeat Hot Spot by putting tape on, but that certainly didn't come up yesterday."
Hot Spot's inventor Warren Brennan suggested earlier in the series that the unusually hot British summer could be causing problems for the system.
But Allardice said: "Even during the Champions Trophy, which was played in June, Hot Spot performed really well - I thought the DRS component of that tournament worked really well.
"Even at Trent Bridge in the first Test match there were a number of pretty fine edges that were confirmed by Hot Spot, so the sequence at Old Trafford last week was a surprise.
"The umpires interpreting the edges when Hot Spot doesn't is difficult, particularly when they're going off stump-mic sounds and trying to make decisions.
"At Old Trafford last week, a lot of the decisions stayed with the on-field umpire, which meant there wasn't enough evidence to overturn them.
"The umpires are trying to interpret it as quickly as possible, that isn't always perfectly handled but I think they did a pretty consistent job at Old Trafford."
Paul Hawkins, the inventor of the Hawkeye technology which forms the other key aspect of the DRS, earlier claimed the issues have occurred because cricket did not carry out the necessary tests prior to implementing the review system.
Hawkins, whose company has produced systems for tennis, cricket and football, said it was as though the DRS system was being tested in live conditions.
He also claimed that while Hot Spot's thermal imaging system was great for television viewers it might not be appropriate to make decisions on whether a batsman was out or not.
Hawkins said: "What cricket hasn't done as much as other sports is test anything. Goal-line technology [in football] has been very, very tested whereas cricket's hasn't really undergone any testing.
"It's almost like it's tested it in live conditions so they are inheriting broadcast technology rather than developing officiating technology.
"Hot Spot is a fantastic piece of technology and has been great for viewers, and in a broadcast world things that work often really adds to the broadcast, whereas the requirements for officiating are obviously different.
"What I would do personally is put it out to a few universities and I am sure they would come up with something, and there's lots of things on the market."
Hawkins also had a very different angle on the issue of tape on bats, suggesting a quick and easy improvement that would work at all levels of cricket would be for batsmen to be obliged to apply tape which would show up when the ball had caught an edge.
He added: "I would insist that all batsmen have micro-pore tape, durable and transparent, and if gets an inside edge onto the pad the batsman can show it to the umpire and say 'I am not lbw'. That's practical engineering."