The Hartlepool United manager watched his side leave north west London defeated on Tuesday night.
Goals from goals from Ryan Glover and Lee Ndlovu pushed the Bees four points clear of Forest Green Rovers and six of York City, but both clubs have played few matches.
Lawrence didn’t tip a team to win the championship but was wowed with what he saw from Dean Brennan’s side.
This weekend Barnet face a tricky trip to Tamworth, while York host Dagenham & Redbridge. Forest Green, meanwhile, travel to Oxford City in the FA Trophy.
"Barnet are a very good team,” he told the Hartlepool Mail.” If you're going to beat them or get a result, you've got to do very well in both penalty areas and we were a little bit short in both.
“They're probably the best team, Barnet. The others are good but I think they're probably the best team. We did our best, we had a go and it wasn't a disgrace by any means."
Pools are striving for consistency, despite just one defeat in nine before their game against the leaders.
"We huffed and puffed and we had a couple of half chances but we didn't really create enough to threaten them,” he said.
“We were honest, we stuck to the game plan and as always they worked hard. It was an honest effort.”
Hartlepool face another long road trip on Saturday when they travel to Essex to face Braintree Town.