Having also beaten Wolves 1-0 at the Reebok Stadium seven days earlier, Bolton's position suddenly looks far healthier as they prepare for tomorrow night's trip to Sunderland.
However, the battle to avoid the drop remains tight, and with 10 games to go, Coyle is not about to let any of his players get complacent about their survival prospects.
"It's always nice to win matches, but there is certainly no leaping about," Coyle said.
"We've won two games back-to-back and it's given us six valuable points, but that's all it is.
"We have got so much hard work ahead of us, starting at Sunderland, and we have to be at our best, as we have been in our last couple of games, to go and earn points.
"We are delighted to get those points on the board, but we are certainly not getting carried away."
Saturday's triumph at Upton Park was also Coyle's first away win in the top flight after he failed to secure victory on the road with former club Burnley earlier in the season, but the 43-year-old was keen to view the result primarily in terms of its significance to Bolton's campaign.
"We talk about this in football, getting monkeys off your back, and it's nice to have had it done, but personal gain is the last thing we are in football for," Coyle said.
"We are here to try and build a football club, to try and keep ourselves in the Premier League and to do that you have to pick up points both home and away.
"We are delighted to have done it to this point, but we have to carry on. We're in a group of teams that are in a real battle at the bottom and the only way that you get out of that is by winning games."
Wanderers will be looking to extend their winning run against a struggling Sunderland side who are without a victory in their last 14 league outings.
With a home match against Wigan to follow, Bolton have the opportunity to consolidate their place around the middle of the table over the next few days, although Coyle is wary of the fact that his side could just as easily find themselves slipping back into the mire if they do not continue to pick up points.
"It was a valuable three points (against West Ham) on the back of the Wolves victory and it elevated us up the league slightly, but we are under no illusions how quickly football can change," Coyle said.
"We are pleased to get the win and I always felt it was coming anyway given the level of performance we were offering up, and we showed that from the first whistle.
"But it is behind us, we can't affect it, and what we can affect is what's in front of us.
"We have got a massive game now at Sunderland, a quality side with some top players, and a magnificent stadium with a great set of supporters.
"We all accept that they have been on an indifferent run, but there is no doubt that Steve Bruce is a top-class manager."
Meanwhile, Coyle has dismissed reports linking Nigeria defender Danny Shittu with a loan move away from the Reebok Stadium.
Asked if there had been any contact from other clubs about the player, Coyle said: "No, there hasn't been. There is always going to be conjecture and I think there was a bit of interest in Danny in January when he was away at the African Nations Cup, but because he was away nothing was going to come to fruition at that point."
He continued: "I'm perfectly happy with Danny here. He is working hard and he's been on the bench a couple of times since he has been back. We don't have great numbers anyway and I don't particularly want anyone going out."