The Foxes at King Power Stadium and in turn stretched their unbeaten run to eight games in all competitions.
A fourth league win on the bounce was secured thanks to goals from Simonas Stankevicius, Danny Drinkwater and Jak McCourt.
“It was tight at half-time in terms of the game being 0-0, but we should have had at least two goals in the first half,” Beaglehole told Foxes Player. “We started a bit sluggishly, which hasn’t been like us of late.
“Scoring first is an important thing. It’s not the be all and end all, but it gives you a great platform to not lose the game.
“We had to reshuffle at half-time. Kieran Kennedy, who played really well, came off and we had young Brandon Fox playing at left-back, as did Alie Sesay in the first half.
“In the second half we started the game like we did at Chelsea. We scored a terrific goal through Simonas right at the start of the second half. From then on I thought we bossed it and we got the second goal.”
While Brandon Fox, who eventually had to be substituted, was off the field receiving treatment for a knock he picked up, City’s back four were breached.
With 16 minutes to play, Kenny McEvoy converted substitute Ismail Azzaoui’s cross and gave Spurs hope, but Leicester added a third from the spot through McCourt in injury time to seal the victory.
Beaglehole added: “I was just disappointed that we conceded when we were down to 10 men [when Brandon Fox went off injured]. We should be able to organise on the pitch and be resilient when that happens.
“That gave Spurs a lift. They had a good spell and came at us – they thought they could probably get something, having not been in the game until that time. But again, we showed our quality. James Pearson did well to get us a penalty and Jak McCourt finished it.
“We’ve scored three goals against what I said was the best team that we’ve played [this season]. They showed tonight the reasons why I said that. It’s another very good result.
“There was some great players on show from both sides. I thought it was a physical and tactical game played on a great pitch. Anybody that likes to watch football saw a good football match.”