Seventh-placed Everton host eighth-placed West Bromwich Albion on Saturday before another home game against struggling Hull City the following weekend.
Following sixth-placed Manchester United's League Cup win last month, a seventh-place finish should be enough for Everton to secure a Europa League third-qualifying round spot if this season's FA Cup winner finishes in the top four.
"I think it's really important first that this Saturday we get a gap between us and West Brom," said Koeman, whose team already has a four-point advantage over their rivals.
"I'm fully confident that if we get six points out of the next two home games, we will be able to look at the competition above us in the table — but we won't make the big mistake of not looking at it game by game.
"That's a big part of what we've tried to do this season, to be the best outside of the six big teams in the Premier League. Then we can be really happy about our first season."
Koeman, who joined the Merseyside club from Southampton at the start of the season, confirmed that Everton would hold talks with midfielder Ross Barkley over a new contract.
Barkley, 23, whose current deal expires in June 2018, was criticised by the Dutchman for his inconsistent performances earlier this season, but responded with a series of strong displays. "He's one of the players who will finish their contract in one year," said Koeman.
Hammers urged to learn from Barca
West Ham United manager Slaven Biic believes other teams, including his own, can learn valuable lessons from Barcelona's thrilling 6-1 Champions League victory over Paris Saint-Germain in midweek.
Trailing the French champions 4-0 from the first leg of their last-16 encounter, Barcelona scored three goals in the last seven minutes of the second leg to seal a 6-5 aggregate win and progress to the quarter-finals.
"It has to put a smile on your face because it was about everything that football is all about; the quality and the great goals," Bilic told reporters ahead of West Ham's Premier League clash with Bournemouth on Saturday.
Bilic said he would use the match in future teams talks. "It's a great game to use in talks with your players on both sides. It was an unbelievable game to watch."
West Ham, who are 11th in the league, will be looking to snap a three-match winless run when they play 14-placed Bournemouth, who are yet to win in 2017. REUTERS
COMMENTS
Comments are moderated and generally will be posted if they are on-topic and not abusive.
For more information, please see our Comments FAQ