The Italian wrote in his programme notes: "I have been pleased with the way my players have responded when we have made changes to the team in the last few weeks. The aim is to come up and play in the Premier League".
Chelsea's loanees were involved in goals at both ends.
Speaking after the game though, former Blues midfielder Lampard - who was making his an emotional return to Stamford Bridge - thought that his new side deserved more from the game than they ultimately got.
"Certainly Frank's got something to do with that [Chelsea allowing Mount and Tomori to play against them in the EFL Cup]", Nicholson told Rams TV.
The Blues have granted permission to Derby to play Mount and Tomori, both on loan from Chelsea, if they wish to during the fourth round EFL Cup tie at Stamford Bridge.
Always positive, always looking forward with impressive energy and - unlike Lampard did in his playing days - often leading the line, Mount helped to suffocate Chelsea with a high press and forced mistakes, particularly from Gary Cahill and Andreas Christensen.
Chelsea went on to win the game in an enthralling encounter, with Tomori left dejected at the final whistle.More news: Lion Air Technical Director Removed Following Orders from Transport Ministry
And it is this game from which Derby can gain confidence, with the Blues switching off defensively at times.
18+ only. Ts&Cs apply. Also combined well with Ruben Loftus-Cheek and Zappacosta on the right.
Scott Carson couldn't keep out Cesc Fabregas' low-effort, but the visitors felt that Alvaro Morata was blocking his view in an offside position, and that Tom Lawrence was fouled in the build-up to the goal.
With rotation likely, Loftus-Cheek will be one of the favourites to start for Chelsea and could yet again find the net. That's why he scored so many goals.
Son scored his first two goals of the season and another of Tottenham's forgotten men, Fernando Llorente, added one in a 3-1 win over West Ham in an all-Premier League London derby at the Olympic Stadium.
"We've put ourselves in great credit, coming to Stamford Bridge and to Old Trafford, but we are back to league action now and we mean business".
From his appearance in the visiting dugout to his lap of appreciation after the final whistle, Derby County's manager was serenaded with chants of "Super, super Frank" and "He's won it all".
Chelsea are still unbeaten in competitive games this season.