Stephen Rice put the Irish part-timers ahead in the Europa League Group A match at White Hart Lane but three goals in five second-half minutes from Roman Pavlyuchenko, Jermain Defoe and Giovani Dos Santos saw Tottenham safely home.
The one sour note for Redknapp was an injury to Aaron Lennon, which saw the England winger substituted at half-time with a groin problem that makes him doubtful for the London derby against Arsenal on Sunday.
Redknapp said: "When we went one down we were concerned because you think maybe it's going to be one of those nights.
"They played their socks off but at half-time we could have been three goals up, we were hitting the woodwork and their 'keeper was making saves.
"I thought it was a matter of time before we scored but they went and scored with their first real strike at goal and you think it's one of those nights, but we stuck a couple of chances away."
Redknapp was pleased with the energy of his side which contained youngsters such as Jake Livermore, Thomas Carroll and Kyle Walker, but he maintained that the Premier League would remain his priority this season.
Redknapp said: "We'll give it (the Europa League) our best shot and see where it takes us. Hopefully we can get through the qualifying group and then look at it again.
"The Premier League is always, for me, the biggest. It's no good at the end of the year people saying Tottenham did well, they got to the semi-final of the Europa League, but finished seventh or eighth in the league again. That's not what I want.
"I want us to have a real go in the Premier League this year and we are capable of doing that. We have fantastic players here, we play some great football, we are a good team."
On Lennon, Redknapp added: "Aaron's okay. He said his groin was a bit stiff and he didn't feel he could play on but I don't think it's too bad. We'll see when he comes in in the morning."
Rovers manager Michael O'Neill, meanwhile, admitted dreaming of what might have been when Rice put his side ahead.
He said: "I kept looking at the clock and it was telling us there was a long way to go still. You do start to think 'can we actually see this out?'
"Ultimately, Tottenham's pace and freshness overcame us in the last half hour but the players gave every ounce of effort. They played with great heart even when the score went to 3-1. They were a credit to themselves, the club and the League of Ireland.
"We were going to get a reaction when we scored. After scoring we played well and they seemed to be knocked out of their stride but you look at the bench and who they can introduce into the game and you begin to fear at that point.
"Everybody will be saying how well we've done and there will be lots of pats on the back but the main thing is the players did themselves justice tonight. We ended up gallant losers."
O'Neill also explained why his side faded in the latter stages.
He said: "In the second half you saw a team which is at the end of its season against one at the start of its season and that's the reality.
"Given the difference in quality between the teams we need to be as fresh as possible. Some of our players have played 50 competitive games this season. It was a huge ask.
"You hope when you score it will give you an energy source but that only lasted 10 minutes or so and in the end we succumbed to a quality side with quality attacking options all over the pitch."
Redknapp, however, admitted he was impressed with Rovers, saying: "They'll get a result somewhere. They are well organised. Great support. We look forward to playing them over in Ireland."
Source: Team Talk
Source: Team Talk