Two Robin van Persie goals cancelled out Steve Morison's opener at Carrow Road and Lambert was pleased to see his team fight for a result until the final whistle.
"They’re a very good side," Lambert admitted during his post-match press conference.
"We were always in the game but you’re never going to keep them out for 90 minutes. You’re never going to have the ball for 90 minutes.
"We tried to get a foothold in the game and stay in it as long as we could [in the second half]. But Arsenal came out strong and got the goal that gave them the lead.
"But give the lads credit – we were in the game until the last minute. We’ve always had a foothold, we’ve never been out of the game, and that’s the pleasing thing if you’re up against a side like them."
Lambert was keen to praise defender Russell Martin's general performance but conceded that his error in the build-up to Van Persie's winner was crucial.
"The difference was the [quality of the] winning goal," he said. "Martin’s general game was excellent but against those types of players you have to make as few mistakes as you can."
The Scottish manager was particularly impressed with the on-fire Van Persie, labelling the Dutchman one of the best forwards in the world.
"They’re a top side and have been in the Champions League for many a year," he said. "They have some world class players, no doubt, and one of the best strikers around [Van Persie].
"He’s scoring for fun and his touch and general play is top drawer."
Morison's goal was his third in as many games and Lambert declared himself delighted with the play of his own centre-forward.
"Morison is at the top of his game at the minute," he said. "He led the line terrifically well and it’s tough to be a lone striker."