Olly Lee broke the deadlock just before half-time, with strikes from Dan Potts, Elliot Lee, Danny Hylton and Luke Berry in the second half rounding off the scoring at the International Stadium.
Although the Hatters were convincing winners come the final whistle, the gaffer felt his side needed to get a stronger grip of the game after the first 45 minutes.
He said: "First half maybe not [we weren't the stronger side], it was a real contest. I thought we had the better of things. We had two real good chances in terms of Dan Potts' header and Luke Berry's chance and then we took the lead. Unfortunate circumstances for Gateshead – but we went in 1-0 up.
"Second half I thought we were outstanding. I thought we moved the ball well, I thought we upped the tempo, some of our play especially for the goals was outstanding.
"We are delighted with the win, we would have been delighted with any win, but to do it in the manner we did it in, we were very happy.
"We have got three games this week, in which everyone is going to play and get involved. We want to move forward in three competitions, three big, big games, so you go as strong as you can in the first one and then Tuesday we will make sure everyone gets game time, but some will double up.
"Then we've got a massive game on Saturday, we know we are going to have to utilise the squad and we did that today as well."