The Irish side took a shock lead at White Hart Lane and were defending doggedly before three goals in six minutes earned Spurs the three points.
"When we went one down you are concerned as you think 'is it going to be one of their nights?'" Redknapp told Sky Sports News.
"But we came in at half-time at 0-0, and I am not being disrespectful to Shamrock - they played okay and worked their socks off - but we could have been at least 3-0. We hit the woodwork and their keeper was making saves.
"I thought it was just a matter of time before we scored but then they scored with their first real strike at goal and then maybe it is one of those nights, but we stuck a couple of chances away and won it."
The draw has left Spurs second in Group A after Rubin Kazan drew with PAOK Salonika.