Marco Silva was impressed by the character of his Everton side in a pulsating second-round Carabao Cup tie after they responded to going behind after 21 seconds to book a meeting with Sheffield Wednesday.

Silva has targeted good cup runs this season as Everton search for their first silverware since the 1995 FA Cup. That appeared to be little more than a distant dream as Lincoln quickly took the lead when Harry Anderson fired home Jack Payne’s cutback.

Lucas Digne equalised with a 30-yard free-kick before Gylfi Sigurdsson put the visitors ahead with a penalty after Morgan Schneiderlin was fouled by Michael O’Connor, firing high into the corner with the England keeper Jordan Pickford running the length of the field to get involved and being booked for his trouble.

It seemed as if Everton had weathered the storm only for Lincoln to level when Bruno Andrade scored the crispest of volleys after a cross from the right was partially cleared.

Back came Everton again with Alex Iwobi nodding home before Richarlison put the game beyond doubt with an unstoppable header.

The final score was harsh on the home side who were still level with nine minutes left but Everton’s dominance paid off and it was the response to their early setback that most impressed Silva.

He said: “We knew before the match how difficult it is always to play this type of competition. We came here to play and do what I ask, for our players to be serious.

“It was not the best way to start the game but after we reacted. We showed good reaction after last Friday [a 2-0 defeat against Aston Villa] as well. We showed personality in the match, which is something that is very important for me.

Quick Guide Carabao Cup third-round draw Show Wolves v Reading, Oxford v West Ham, Watford v Swansea, Brighton v Aston Villa, Sheff Utd v Sunderland, Colchester v Tottenham, Portsmouth v Southampton, Burton v Bournemouth, Preston v Man City

MK Dons v Liverpool, Man Utd v Rochdale, Luton v Leicester, Chelsea v Grimsby or Macclesfield, Sheff Wed v Everton, Arsenal v Nottm Forest , Crawley v Stoke Ties to be played week commencing 23 September

“We deserved to win. Even if I knew, and the players knew, before this match it was our obligation to come here and keep playing in this competition, but we did it in a good way. Be serious, respect ourselves and the competition and showing for our fans what we said before: our ambition is big. We want to do everything we can do to keep playing in the Carabao Cup.”

His opposite number, Danny Cowley, had nothing but pride in his players who, he said, had shown grit, determination and resilience.

They had broken the game down into six 15-minute periods and at 2-2, he said, they “smelled blood” and felt they could win the game but it was not to be as they went toe-to-toe with their Premier League opponents.

It was also the first time that Cowley had lost three successive games in his managerial career after they went down to MK Dons and Doncaster.

He said: “You have to respect Everton – a top Premier League team with world-class players. The fact they have come here with their full squad we should be really proud of.

“We played them in the FA Cup last season and off the back of that they have shown us the respect to bring the squad they did.

“Credit to them because they played right at the top of their game. It was a really good game, some really good goals and a great advert for the Carabao Cup.”