City sit third in the table after Saturday’s 2-1 win over Leicester and have just two matches remaining.
West Brom visit the Etihad Stadium on Tuesday, before City’s final game next weekend away at Watford brings the curtain down on Pep Guardiola’s first campaign in charge.
If City can take maximum points from those two fixtures, they are assured of a third-place finish, thus avoiding the need to qualify for the group stages of next season’s Champions League.
“We have to be confident,” the Belgian said after the win over Leicester.
“We’re in a good position for that target, but games are difficult. The Leicester game was, I’m sure Tuesday will be. We need to rest now.
“Today was a harder one of our last games. But we have to feel confident with one more home game and then we’ll see.
“We have to win that home game and the Watford game we know is going to be difficult but we’re perfectly capable of getting the result we need.”
City will finish the season without a major trophy, despite winning their first 10 games in all competitions and setting the early pace in the Premier League.
It’s left many disappointed - but Kompany is already looking forward with optimism and he believes finishing the campaign strongly will provide the momentum needed to make a strong start next season.
“A lot of times you tend to focus on just getting over the line but in reality it can be a way to build and be strong next season,” he said.
“I do believe that. Let’s finish this season strongly and keep the confidence high for next season, which is going to start pretty soon.”
Leicester, last season’s title winners, provided a stern test for City, who needed to show plenty of resilience to dig in and seal the three points.
They found themselves 2-0 up thanks to goals from David Silva and Gabriel Jesus, but Shinji Okazaki’s brilliant volley just before half time cut the arrears and Leicester grew in confidence.
The second half saw a much-improved Foxes side take the game to City – but the Blues back four stood firm.
“We made a couple of good challenges in the box,” he said.
“We defended pretty deep at some stages and we got on the end of those balls.
“That’s not been the case too often this season but maybe that was the difference today.”
Leicester had a chance to equalise when Riyad Mahrez was brought down inside the box with 12 minutes remaining.
The Algerian, a fine penalty taker, stepped up to take the spot kick and scored – but referee Bobby Madley ruled it out because Mahrez had slipped and touched the ball twice.
It was a bizarre incident, but Kompany believes the referee made the correct call.
“Yeah, I saw the ricochet and I was pretty glad of that!” he said.
“Well, rules are the rules.
“It’s happened before [in a game I’ve played in] but the referee didn’t spot it, so fair play to the referee for spotting what was ultimately an important fact in the game for us.
“We probably got away with it but if you reflect on the entire game I thought we were the better team, although Leicester were solid and threatening.
“But I was happy with the way we defended crosses, the way we put in the last challenges to clear our lines.
“It wasn’t as comfortable as it was last week [in the 5-0 win over Crystal Palace] but it was exactly what we needed to win the game.”
