"He's given Gareth a lot to think about with his performance the other night," Allardyce told reporters.
"I know people have gone on about him conceding goals for Everton this season but that's not the stat you look at as a goalkeeper, you look at the sort of saves he makes... he's always there when needed.
"He's been extremely busy - far too busy on some occasions - and we've managed to quell that lately... that helps the goalkeeper," he added.
Pickford has made 103 saves in 31 games - behind only Swansea City's Lukasz Fabianski (106) and fellow England keeper Jack Butland (112) - although the Merseyside club have conceded 50 goals this season.
The 24-year-old could face another busy evening at Goodison Park on Saturday with the visit of Premier League champions-elect Manchester City, who have scored a league-high 85 goals in the campaign.
Pep Guardiola's side needed an 82nd-minute equaliser in the reverse fixture this season and Allardyce said ninth-placed Everton had to approach the game with a positive attitude.
"We have to say we can challenge them and play against them. You can get a result but we'll have to play our best," he added.
Idrissa Gueye will be assessed after picking up a hamstring injury in the 2-1 win over Stoke City this month and fellow midfielder Tom Davies is fit after recovering from a neck injury.
(Reporting by Shrivathsa Sridhar in Bengaluru, editing by Ed Osmond)
