Cook tapped in the winner from close range six minutes before half-time after a shot from Alan McCormack was parried by the Barnet goalkeeper.
Coach Joaquin Gomez took charge of the game at Barnet, who last night appointed former Wolves boss Mark McGhee as their new manager.
Gomez told lutontown.co.uk: “It wasn’t a great game in all honesty. The pitch wasn’t great, but you have to deal with it and get on with it.
“They had quite a young squad out and with the circumstances they have around the place at the moment with the new manager, they were really up for it and started really well.
“It took us by surprise for the first ten minutes or so, and we didn’t start that well. But as the first half went on, we dominated the game and were solid.
“It wasn’t as pretty as some the other games, but we were very competitive after the first ten minutes.
“In the second half there wasn’t much quality in the game, but we had spells of defending very well. We were very competitive, very professional and saw the game out.”
One of the big pluses of the match was McCormack getting an hour-long run-out on his return to action following a hernia operation, as well as players like Lawson D’Ath, James Justin, Aaron Jarvis and Cook getting important game time.
Gomez added: “What we wanted from the game was to make it as competitive as a Tuesday training session for us, and the boys always give us that.
“Players like Macca, Lawson, Jarvo and Cookie – lads who haven’t had many minutes recently, whether coming back from injury or haven’t been in the team – all need to get up to speed for when they are called upon.
“JJ, Cookie and Jarvo all got 90, and Macca played for around 60, which was longer than planned but he felt good, so he’ll benefit from that.
“The goal was second phase from a corner. The ball fell to Macca on the edge of the box, he had a shot and from the rebound Cookie tucked it in.
“It wasn’t the prettiest of goals or games, but it was a good work-out and we won, so it was all positive.”
TOWN TEAM: Shea, Justin, Musonda, Famewo, Senior, McCormack, Cotter, Douglas, D’Ath, Cook, Jarvis. Subs: James, Isted, Peck, Neufville, Read
