The Tigers, whose highest league finish came last season when manager Steve Bruce led his side to 16th, head to Liverpool tomorrow sitting 11th in the table with 10 points from their opening eight games.
However, with just five points separating Arsenal in seventh from Newcastle United in the final relegation place, the concertina effect in the top flight means teams can significantly move up or down the table courtesy of just one result.
Elmohamady, who is in line to make his 65th consecutive league appearance at Anfield tomorrow, said: “The season is going well. But I do feel after eight games that we should really be in the top six.
“If we had got all the points we should have taken (Hull would be top six).
“We have new players and we are getting better and better all the time. The goals are going in and that is pleasing. Every team has to have that attacking threat.
“Look at Arsenal (last Saturday). In the last second we conceded, but we got two goals against a very good team that played in the Champions League a few days after playing us.
“That is what we are up against. It was a good experience. We are learning with every game and everyone looks forward to the next game coming round.
“The next four or five games will be very important. They are all tough, as every game in this league is tough.”
Asked what a realistic target for the Tigers would be this term, Elmohamady replied: “We just want to finish as high as possible.
“Top 10 would be a fantastic achievement for us. I believe that is a realistic target with this squad. We deserve much more than last year.”
Elmohamady’s belief that Hull have not had their just reward in terms of points this term relates to the number of times winning positions have been surrendered.
Danny Welbeck’s stoppage-time equaliser at the Emirates was the fourth time in eight games that Hull have had to settle for a point after being ahead.
Almost a week on from the 2-2 draw in north London, Hull head to Anfield without Nikica Jelavic (knee) and Michael Dawson (ankle) with the duo expected to be out for up to six weeks after picking up injuries at the Emirates.
Goalkeeper Steve Harper (torn bicep) will also be missing, meaning Eldin Jakupovic is in line for only his second start in the Premier League.
Despite missing several key players, Elmohamady insists Hull will travel buoyed by the manner of last weekend’s display.
He said: “To go to Arsenal and get a point like we did is good, although of course we could have had all three and that was disappointing.
“We have conceded in the last minute three or four times now.
“But it was still a good point, as we worked very hard from the first minute to the last minute in a very difficult place to play.
“In the league last season, the games against Arsenal were not too close. The FA Cup final was, but not the league. So that (last Saturday) was a big plus for us.
“We got two very good goals and caused them problems. That has to help our confidence going into a big game like Liverpool.
“We will work just as hard against Liverpool. I know everyone will give 100 per cent. We are looking forward to returning to Anfield and playing like we did at Arsenal.”
For Elmohamady, a £2.5m signing after impressing hugely on loan in Hull’s promotion season, the trip to Merseyside should continue an amazing unbroken run of league starts stretching back to February, 2013.
He added: “Touch wood, I can keep playing. As a player, you want to play. To play so many times in a row (64) is brilliant for me. It makes me very happy.
“I enjoy it here and the manager gives me confidence every time I play.
“So do the players who play with me. That is fantastic.
The fans are great to me, too. I am still young at 27 and if you didn’t play every game at my age, when will you play?
“I want to play and it is great the manager shows such faith in me.
“I just want to keep going, look after myself inside and outside the game. I want a long career and I want to stay in the Premier League.
“For me, it is the best league in the world and I want to stay here for a long time.”