Manchester City will take on Crystal Palace in the Premier League on Sunday.
Potter was also delighted with the way that Steele redeemed himself in the shoot-out after an error which led to the home side's equaliser.
And Webster netted the deciding penalty - the 14 spot kick of the shoot-out - to seal it 4-3 and seal Albion's progression. "I said to the players we will have to be at a high standard to compete against them". We made it hard for ourselves and to concede in the last second was a blow.
The visitors thought they had won the tie when Solly March struck from the edge of the penalty area with just 10 seconds of the 90 minutes remaining.
"Newport made it tough for us though, so we have to give huge credit to them too".
Pep Guardiola has warned that momentum can disappear in "one instant" as he prepares his Manchester City side to face Brighton after six successive wins in all competitions.
Neil Critchley's League One side have already travelled to Sussex in the FA Cup this season, having won 3-0 at National League South side Eastbourne Borough in the First Round back in November.
Brighton appeared to have sealed a late victor when Solly March scored a 90th minute. cracker, but Newport pushed his way into the game with one of the game's last chances.
But the match went to extra-time when Steele flapped at Shephard's cross and the ball went in off Webster.