The Chelsea star, who captained the England side at the Stadio Olimpico di Seravalle, scored his 28th international goal and in the process surpassed the previous record of 27 goals for a midfielder held by David Platt, now the Manchester City first-team coach.
England heads to group leaders Montenegro on Tuesday where manager Roy Hodgson is expected to recall captain Steven Gerrard to the starting lineup, thus throwing Lampard's starting position into doubt.
"It feels very good to be England's highest midfield goalscorer. I'm very proud of that achievement. All my career, I've looked to score goals. It was great to be up there with the likes of the Bryan Robsons and the David Platts," Lampard told Sky Sports News.
He added, "Now I am above them and it was also an honor as always to wear the armband for your country. Stevie will be back on Tuesday so he will take it, but I am really pleased with how I played. We said if we approached it in the right way, then we would have no problems and that is what happened."
Tuesday's opponents Montenegro beat Moldova 1-0 in the other game in England's group to stay two points clear of Hodgson's men.
"Everyone who played did themselves a favor. Everyone turned up but Montenegro is a different game so we might approach it in a slightly different way," Lampard said.
"It was a great confidence boost for us to score so many goals. Whoever is asked, will be ready on Tuesday."