The Argentine, whose career has been disrupted by injury woes since late 2016, netted Spurs' second against the League Two outfit in a 2-0 win.
"I was out for a long time and it was difficult for me but I am back playing now and it is good to get a goal. We have a very good team and we need everyone fit to fight for places," BBC Sport quotes Lamela as saying.
Lamela doubled his side's advantage over Newport in the 34th minute, adding to the lead they secured when Dan Butler put through his own net.
Spurs will take on Rochdale in the fifth round of the FA Cup.