Chelsea and Arsenal will go head to head on Wednesday for a place in the Carabao Cup final with Antonio Conte admitting neither team can compete financially with the might of the two Manchester clubs.

The Premier League champions had never been in contention to sign Alexis Sánchez this month, despite declaring an interest last summer, after it became clear the forward’s wage demands – he is believed to command a basic salary of around £300,000 a week – and agent fees would be prohibitive. Manchester City drew the same conclusion, with Manchester United, who made the most money of any club in the world last year, finalising a deal on Monday.

Chelsea still hope to secure the signings of Edin Dzeko and Emerson Palmieri from Roma for an initial £44m, yet City’s outlay in the market over recent seasons still dwarfs that of the Stamford Bridge club, for all their status as one of the original nouveaux riche under the ownership of Roman Abramovich.

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“In this moment, there are two teams in this league who are ‘top’,” Conte said. “The others have to fight for a place in the Champions League. Last season we did a fantastic job and did a little miracle. This season is showing this.

“We won the league and reached the FA Cup final, and finished with a profit of £50m in the transfer market [actually £69.2m, largely as a result of Oscar’s sale to Shanghai SIPG]. In the past, this had never happened but the situation changed. What happened three years, 10 years or eight years ago was totally different. Now we have to fight and give our all for Chelsea because United and Manchester City will stay there. We’ll have to make a success not with money but with work.

“It’s not simple [to finish above the Manchester clubs] because these big teams continue to improve and invest a lot of money, and there is this gap. These two big clubs can become seriously dangerous for other teams in the world: they are very strong already and want to invest. Look at Alexis Sánchez. Only one or two clubs can pay this type of salary. This is the market. If you want to buy Neymar, you must be ready to give him €25m in wages. If you want to buy Messi, Ronaldo, now Sánchez, you must be ready to pay his salary. We never were in this race for Sánchez, ever, and one of the reasons was this amount of salary.”

Chelsea still broke their own transfer record last summer with the purchase of Álvaro Morata, who will miss the second leg of the Carabao Cup semi-final with a back injury, from Real Madrid. “But to spend €55m on a young striker like Morata, and selling an older player in Diego Costa [to Atlético Madrid] for €60m … that was a good sign for the club,” Conte said. “When you go in the transfer market you have to know that, if you want the best, you have to be prepared to spend a lot of money. Otherwise you go in the middle and spend £20-30m, and find other ways to stand up and fight.

“We need to improve with this team. To improve the squad. To create this basis. In the last couple of years, we lost a lot of old players who wrote the history of this club. I don’t like this word ‘transition’ but sometimes you have to see the truth. For me, this is already a good season. I’m doing a fantastic job, the same as my players. It’s not important if you reach the final or win a trophy or win the league. The most important thing is to see if the coach and players are working very hard and very well.”

Palmieri’s imminent purchase has led to Kenedy joining Newcastle on loan for the rest of the season. Conte confirmed Michy Batshuayi “will go on loan” if a replacement is purchased. Dzeko’s arrival will see Chelsea relax their policy of offering one-year contracts to players over the age of 30 – the Bosnian is 31 – though negotiations continue and Roma are still considering selecting the forward against Sampdoria on Wednesday.