Two goals from leading scorer Amari Morgan-Smith put Town in front, before Ed Asafu-Adjaye was sent off midway through the second half after picking up two bookings in as many minutes.
Hosts Telford upped their game to put the Luton backline under some sustained pressure, but Hatters held firm to move up to third in the table.
Brabin said: “I thought it was a spirited performance. I’m proud of the fact we’ve won two games back-to-back. We’ve kept clean sheets, but we’ve shown a lot of character in the last two games. It’s hard when you’re down to 10 men and I thought we showed a great deal of spirit and defended fantastically. I thought the two centre-halves were like rocks at the back.
“After going 2-0 up and then going down to 10 men, we needed a good solid response and all of the lads, even the subs who came on, worked really hard and played their part in that last 20 minutes.
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The boss had no complaints with Town’s first red card of the season though as he continued: “I thought it was a sending off. I’ve spoken to Ed about doing the right thing and thought he could have cleared it.
“I’d have to look at it again, but I thought he tried to keep possession rather than just clear the ball. It hasn’t fallen kindly and he’s ended up giving a foul away.
“It’s fresh in the referee’s mind that he’s just booked him a couple of minutes earlier, so in terms of that we’ve got no arguments.
“I thought the referee and his officials had a very good game. It was a difficult game as it was quite end-to-end and it was quite a tough contested match, but I thought they handled it really well.”
Although Luton were worthy winners on the night, there was still plenty of room for improvement in Brabin’s eyes.
He said: “Sixty per cent of the game there was some fantastic football played by us.
“We’ve done a few of the things that we’ve been punished for, so I was delighted we were still 1-0 up with some of the mistakes we made in the first half.
“We’ve addressed that at half time. I didn’t even have to say too much, the lads knew.
“We’ve come out, scored the second, played some good football, and I thought from that point, we could have gone on from strength-to-strength. The sending off put us under a bit of pressure, but I thought we were fantastic.”
The boss also reserved words of praise for Town’s supporters too, as once again they turned up in their numbers.
He added: “It was brilliant. They were in good spirits and just coming out it gives you a little bit of a lift as they were there in their numbers. I thought it was a good night, a good three points and lets hopefully continue this little run.”