Although Town had already triumphed at Barnsley on their travels this term, the Tykes were, like Luton, one of the newly-promoted teams from League One.
However, against a side who won the Premier League in 1995 and dominated possession, with 66 per cent of the ball, for Town to emerge victorious, Tunnicliffe said: “It’s a massive mental step for us to take to prove that we can go to these places and win games, quite well as well.
“I think we were in control, obviously they had more of the ball, but out of shape, I think we were quite comfortable.
“We got the two goals which is never easy and probably hung on for the last 10 minutes when they were throwing everything at us, but that’s another step that we’ve taken where we can dig in and not concede.
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“We’re massively pleased, I think it’s probably one of the tougher places to go in the league, with a team that’s really good at everything.
“I don’t think there was much of a weakness we could pick out before the game.
"So to come away from there with all three points is a massive boost for us to believe that we can go anywhere and win games.”
Despite Rovers having more goal attempts, registering15 to Luton’s eight, they only had two shots on target, with Town seeing five test former Luton stopper Christian Walton, as Tunnicliffe thought visiting keeper Simon Sluga had a quieter afternoon than expected.
He said: “I don’t think he had many saves to make, they didn’t get many shots on target, so that’s a credit to us that when they did have shooting chances, we put them under pressure.
"We stopped balls in the box, so when they did get crosses in, we defended the box well and second balls, I think we were dangerous on the break, which we showed a few times.
"So all round, it was a good solid away performance and that’s what you need in this league.
“That’s probably the best feeling we've had in the changing room afterwards too.
"If any outside people were in there they would have seen how buzzing the lads were.
"The gaffer said it after the game, this is the best feeling, you can’t buy that feeling, when you know you’ve worked hard, you’ve dug in and you’ve earned the result.
"It’s probably the best feeling in the game to go away from home and dig in like that, not concede, stand strong and come away with the three points, there’s no better feeling."
The Hatters had gone into the game on the back of three successive defeats in all competitions, but Tunnicliffe insisted that the display they put on showed morale hadn’t been hit by the trio of reverses.
He added: "I think by the performance, we weren’t lacking in confidence.
"We went there and although we didn’t have as much of the ball as we usually do, or we like to have, I think we were in control of what we were doing.
"So I don’t think confidence was low, but two defeats, you need to start picking up points in this league quite quickly, otherwise you get separated from the rest.
"It was a massive result and the start of a big week for us we’ve got three games in a week."