Skipper Ronnie Henry put in his best performance in a Luton shirt as the 28-year-old defender made a number of crucial interventions.
Goalscorer Shaw hailed his contribution, saying: “Ron is one of the biggest winners personality-wise I think I have ever come across.
“Training, he really gives his all every day, and the match summed him up. The balls that are coming across the front post, he’s coming in from right-back and defending at the near post.
“It’s brilliant for him, for us – it helped us in the long run.”
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Keeper Mark Tyler was also to the fore with a number of fine saves.
Shaw said: “There were two unbelievable saves by Mark Tyler.
“The first one, not very many people noticed it, but he got a finger on to it and took it on to the post, and the second one as well.
“Sometimes you have to ride your luck to win games, but when you’ve got somebody like him in-between the sticks it gives you a great platform to play from.
“I wanted to run back all the way from the forward line to give him a hug, it was unreal the saves from where they were.
“He’s a great keeper. I’ve admired him from afar for a long time and it’s great to be playing in the same team as him.”
Fellow striker Andre Gray scored Town’s first and laid on the second for Shaw, who said: “Andre’s been brilliant.
“He really showed what everybody knows he can do.
“He’s fast, he’s strong he really puts people under pressure.
“We had a little laugh at the end because he absolutely rapped the cross at me, but we also said if he didn’t hit it that hard it possibly wouldn’t have gone in.
Town defended tigerishly on the day and Shaw was impressed with the contribution of young midfielder Matt Robinson after Alex Lawless was forced off through injury.
“We were confident because we were playing really solidly defensively and I think it showed how far we’ve come defensively as a team, we worked really hard,” Shaw said.
“The lads at the back who have come in after not playing for a few weeks have done brilliant.
“Then the the midfield as well with young Matty Robinson coming in, we looked solid and I think it gave us a great platform to go forward and keep searching for that goal.”
There was also a promising debut from new signing Arnaud Mendy who caught Shaw’s eye in Town’s 4-1 home victory over Macclesfield earlier this season.
He added: “I was really impressed. I remember thinking after the game their midfield were really strong, really good.
“Again, he’s shown exactly what he’s about. He’s strong on the ball, he gives it simple and he’s a fit lad.
“He’s a hard worker and he’s a big strong lad as well. It’s something we wanted in there, I think, a big dominant presence.
“He’s had a fantastic debut, it’s great to come in and win a cup tie like that and that will spur him on, and do us well.
“I wouldn’t say he’s the missing piece, we are doing really well, the squad is strong throughout.
“I’m sure the manager will keep looking to add pieces if he thinks that we need them.
“I’m sure the reason we haven’t brought many in is because he knows that the squad that we’ve got is relatively strong and strong enough for this standard and he genuinely believes it and so do we.
“Sometimes you can look around and think we don’t really need to add anybody, but when you bring somebody in of that kind of quality it just gives you that little lift.”
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